范·斯霍滕圆锥曲线作图法:椭圆、双曲线与抛物线
2014-09-16 15:23
本范例展示了范·斯霍滕(van Schooten)用于构造椭圆、双曲线和抛物线的经典连杆机构。通过GeoGebra的动态几何功能,利用点、线段、垂线、圆及轨迹等命令,模拟机械连杆的运动过程,直观演示圆锥曲线的几何生成原理。该作图法结合了解析几何与参数曲线的概念,适合用于探究圆锥曲线的定义及其几何性质。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="4.4" version="4.4.5.0" id="5175a36e-1dbd-4fe8-8fdc-baeacd4d84e9" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="849" height="812" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.31802120141342755" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1" size="400" window="572,249,700,550" />
<view id="4" toolbar="0 59 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 | 1011 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="838" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="270" window="100,100,250,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 39 59 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 66 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6 | 100001 | 100002" position="1" help="false" />
<input show="true" cmd="true" top="false" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="20"/>
<graphicsSettings javaLatexFonts="false"/>
</gui>
<euclidianView>
<size width="838" height="674"/>
<coordSystem xZero="521.561363614222" yZero="335.79762135801883" scale="32.70031863206509" yscale="32.700318632064764"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="10"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="line" label="a">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="0.0" y="1.0" z="-5.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="explicit"/>
</element>
<command name="Point">
<input a0="a"/>
<output a0="K"/>
</command>
<element type="point" label="K">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="19" y="6"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="6.0" y="5.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="a"/>
<output a0="J"/>
</command>
<element type="point" label="J">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-4.0" y="5.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="J" a1="K"/>
<output a0="l"/>
</command>
<element type="segment" label="l">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="10.0" z="-50.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="l"/>
<output a0="G"/>
</command>
<element type="point" label="G">
<show object="true" label="true"/>
<objColor r="255" g="127" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-17" y="-4"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="3.346714679362948" y="5.0" z="1.0"/>
<pointSize val="9"/>
<pointStyle val="0"/>
</element>
<command name="OrthogonalLine">
<input a0="G" a1="a"/>
<output a0="b"/>
</command>
<element type="line" label="b">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.0" y="0.0" z="3.346714679362948"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<element type="point" label="C">
<show object="false" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="2.0" y="6.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="E">
<show object="false" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="6.0" y="6.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="C" a1="E"/>
<output a0="f"/>
</command>
<element type="segment" label="f">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="4.0" z="-24.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="OrthogonalLine">
<input a0="C" a1="f"/>
<output a0="g"/>
</command>
<element type="line" label="g">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-4.0" y="0.0" z="8.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="OrthogonalLine">
<input a0="E" a1="f"/>
<output a0="h"/>
</command>
<element type="line" label="h">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-4.0" y="0.0" z="24.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Circle">
<input a0="C" a1="0.2"/>
<output a0="k"/>
</command>
<element type="conic" label="k">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="39.96" A3="0.0" A4="-2.0" A5="-6.0"/>
<eqnStyle style="specific"/>
</element>
<command name="Circle">
<input a0="E" a1="0.2"/>
<output a0="p"/>
</command>
<element type="conic" label="p">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="71.96000000000001" A3="0.0" A4="-6.0" A5="-6.0"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="k" a1="g"/>
<output a0="F_1" a1="G_1"/>
</command>
<element type="point" label="F_1">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.0" y="5.8000000000000025" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="G_1">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.0" y="6.1999999999999975" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="p" a1="h"/>
<output a0="H" a1="I"/>
</command>
<element type="point" label="H">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="6.0" y="5.80000000000002" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="I">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="6.0" y="6.19999999999998" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="G_1" a1="I"/>
<output a0="i"/>
</command>
<element type="segment" label="i">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.7763568394002505E-14" y="4.0" z="-24.80000000000003"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="F_1" a1="H"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.7763568394002505E-14" y="4.0" z="-23.19999999999997"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="F_1" a1="G_1" a2="I" a3="H"/>
<output a0="poly1" a1="f_1" a2="g_1" a3="i_1" a4="h_1"/>
</command>
<element type="polygon" label="poly1">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="false" label="false"/>
<objColor r="255" g="153" b="153" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="f_1">
<show object="false" label="true"/>
<objColor r="255" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="-0.399999999999995" y="0.0" z="0.79999999999999"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="g_1">
<show object="false" label="true"/>
<objColor r="255" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="1.7763568394002505E-14" y="4.0" z="-24.80000000000003"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="i_1">
<show object="false" label="true"/>
<objColor r="255" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-80" y="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.3999999999999595" y="0.0" z="-2.39999999999975"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="h_1">
<show object="false" label="true"/>
<objColor r="255" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="1.7763568394002505E-14" y="-4.0" z="23.19999999999997"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Semicircle">
<input a0="F_1" a1="G_1"/>
<output a0="q"/>
</command>
<element type="conicpart" label="q">
<show object="false" label="true"/>
<objColor r="255" g="153" b="153" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="39.96" A3="0.0" A4="-2.0" A5="-6.0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Semicircle">
<input a0="I" a1="H"/>
<output a0="r_1"/>
</command>
<element type="conicpart" label="r_1">
<show object="false" label="true"/>
<objColor r="255" g="153" b="153" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="71.96000000000001" A3="0.0" A4="-6.0" A5="-6.0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="numeric" label="r">
<value val="5.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="3" max="11" absoluteScreenLocation="true" width="200.0" x="1001.0" y="57.0" fixed="true" horizontal="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="Circle">
<input a0="G" a1="r"/>
<output a0="d_1"/>
</command>
<element type="conic" label="d_1">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="11.200499145063441" A3="0.0" A4="-3.346714679362948" A5="-5.0"/>
<eqnStyle style="specific"/>
</element>
<command name="Point">
<input a0="b"/>
<output a0="P_1"/>
</command>
<element type="point" label="P_1">
<show object="false" label="false"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="18" y="54"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="3.346714679362948" y="-7.074132474537535" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="LaTeX">
<input a0=""L""/>
<output a0="text2"/>
</command>
<element type="text" label="text2">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.0" size="0" style="0"/>
<startPoint x="-4.612921325976653" y="6.030613263113236" z="1.0"/>
</element>
<command name="工具2">
<input a0="J" a1="K"/>
<output a0="poly2" a1="s" a2="t"/>
</command>
<element type="polygon" label="poly2">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="160" g="160" b="160" alpha="0.5"/>
<layer val="0"/>
<labelOffset x="-10" y="-27"/>
<labelMode val="0"/>
</element>
<element type="conicpart" label="s">
<show object="false" label="false"/>
<objColor r="255" g="153" b="153" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="40.96" A3="0.0" A4="4.0" A5="-5.0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="conicpart" label="t">
<show object="false" label="false"/>
<objColor r="255" g="153" b="153" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="60.96" A3="0.0" A4="-6.0" A5="-5.0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="工具2">
<input a0="G" a1="P_1"/>
<output a0="poly8" a1="g_2" a2="h_2"/>
</command>
<element type="polygon" label="poly8">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="160" g="160" b="160" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="conicpart" label="g_2">
<show object="true" label="false"/>
<objColor r="255" g="153" b="153" alpha="0.5"/>
<layer val="0"/>
<labelOffset x="37" y="67"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="36.16049914506344" A3="0.0" A4="-3.3467146793629485" A5="-5.0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="conicpart" label="h_2">
<show object="false" label="false"/>
<objColor r="255" g="153" b="153" alpha="0.5"/>
<layer val="0"/>
<labelOffset x="51" y="28"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="61.20384941236999" A3="0.0" A4="-3.3467146793629485" A5="7.074132474537535"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="B">
<show object="false" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0.7764581037411948" y="3.929412899659891" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="D">
<show object="false" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0.7764581037411948" y="0.9294128996598912" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="B" a1="D"/>
<output a0="n"/>
</command>
<element type="segment" label="n">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.0" y="0.0" z="-2.3293743112235843"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="n"/>
<output a0="F"/>
</command>
<element type="point" label="F">
<show object="true" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-32" y="20"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0.7764581037411948" y="3.5701074167117453" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="F" a1="r"/>
<output a0="c"/>
</command>
<element type="conic" label="c">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="-11.651445846274415" A3="0.0" A4="-0.7764581037411948" A5="-3.5701074167117453"/>
<eqnStyle style="specific"/>
</element>
<command name="Circle">
<input a0="G" a1="r"/>
<output a0="d"/>
</command>
<element type="conic" label="d">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="11.200499145063441" A3="0.0" A4="-3.346714679362948" A5="-5.0"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="c" a1="d"/>
<output a0="A" a1="L" a2="" a3=""/>
</command>
<element type="point" label="A">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.26167104369231176" y="8.461149010610633" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="L">
<show object="true" label="false"/>
<objColor r="160" g="160" b="160" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4.3848438267964545" y="0.10895840610111103" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="工具2">
<input a0="F" a1="A"/>
<output a0="poly3" a1="e" a2="c_1"/>
</command>
<element type="polygon" label="poly3">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="160" g="160" b="160" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="conicpart" label="e">
<show object="true" label="false"/>
<objColor r="255" g="153" b="153" alpha="0.5"/>
<layer val="0"/>
<labelOffset x="-72" y="35"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="13.308554153725586" A3="0.0" A4="-0.7764581037411947" A5="-3.5701074167117453"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="conicpart" label="c_1">
<show object="true" label="false"/>
<objColor r="255" g="153" b="153" alpha="0.5"/>
<layer val="0"/>
<labelOffset x="-47" y="64"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="71.61951431486433" A3="0.0" A4="0.2616710436923117" A5="-8.461149010610633"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="工具2">
<input a0="F" a1="L"/>
<output a0="poly4" a1="e_1" a2="k_1"/>
</command>
<element type="polygon" label="poly4">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="160" g="160" b="160" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="conicpart" label="e_1">
<show object="true" label="false"/>
<objColor r="255" g="153" b="153" alpha="0.5"/>
<layer val="0"/>
<labelOffset x="-11" y="69"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="13.308554153725584" A3="0.0" A4="-0.7764581037411948" A5="-3.5701074167117453"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="conicpart" label="k_1">
<show object="true" label="false"/>
<objColor r="255" g="153" b="153" alpha="0.5"/>
<layer val="0"/>
<labelOffset x="17" y="-27"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="19.198727319655077" A3="0.0" A4="-4.3848438267964545" A5="-0.10895840610111082"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="工具2">
<input a0="A" a1="G"/>
<output a0="poly5" a1="p_1" a2="q_1"/>
</command>
<element type="polygon" label="poly5">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="160" g="160" b="160" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="conicpart" label="p_1">
<show object="true" label="false"/>
<objColor r="255" g="153" b="153" alpha="0.5"/>
<layer val="0"/>
<labelOffset x="-40" y="-18"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="71.61951431486432" A3="0.0" A4="0.2616710436923104" A5="-8.461149010610633"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="conicpart" label="q_1">
<show object="false" label="false"/>
<objColor r="255" g="153" b="153" alpha="0.5"/>
<layer val="0"/>
<labelOffset x="-60" y="51"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="36.16049914506345" A3="0.0" A4="-3.346714679362949" A5="-5.000000000000002"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="工具2">
<input a0="L" a1="G"/>
<output a0="poly6" a1="s_1" a2="t_1"/>
</command>
<element type="polygon" label="poly6">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="160" g="160" b="160" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="conicpart" label="s_1">
<show object="false" label="true"/>
<objColor r="255" g="153" b="153" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="19.19872731965507" A3="0.0" A4="-4.384843826796454" A5="-0.10895840610111096"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="conicpart" label="t_1">
<show object="true" label="false"/>
<objColor r="160" g="160" b="160" alpha="0.5"/>
<layer val="0"/>
<labelOffset x="-70" y="38"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="36.16049914506343" A3="0.0" A4="-3.3467146793629476" A5="-5.0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Line">
<input a0="A" a1="L"/>
<output a0="a_1"/>
</command>
<element type="line" label="a_1">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="8.352190604509522" y="4.646514870488766" z="-37.12932826662449"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Midpoint">
<input a0="A" a1="L"/>
<output a0="M"/>
</command>
<element type="point" label="M">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.0615863915520714" y="4.285053708355872" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="M" a1="9"/>
<output a0="c_2"/>
</command>
<element type="conic" label="c_2">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="-58.3881762666729" A3="0.0" A4="-2.0615863915520714" A5="-4.285053708355872"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="c_2" a1="a_1"/>
<output a0="N" a1="O"/>
</command>
<element type="point" label="N">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2.3138109076136812" y="12.149905803243165" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="O">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="23" y="-10"/>
<labelMode val="0"/>
<coords x="6.436983690717823" y="-3.5797983865314214" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="工具2">
<input a0="N" a1="O"/>
<output a0="poly7" a1="d_2" a2="e_2"/>
</command>
<element type="polygon" label="poly7">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="160" g="160" b="160" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="conicpart" label="d_2">
<show object="false" label="true"/>
<objColor r="255" g="153" b="153" alpha="0.5"/>
<layer val="0"/>
<labelOffset x="-8" y="42"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="152.93393194387397" A3="0.0" A4="2.313810907613681" A5="-12.149905803243165"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="conicpart" label="e_2">
<show object="false" label="false"/>
<objColor r="160" g="160" b="160" alpha="0.5"/>
<layer val="0"/>
<labelOffset x="7" y="41"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="54.2097155227802" A3="0.0" A4="-6.436983690717824" A5="3.5797983865314205"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Intersect">
<input a0="b" a1="a_1"/>
<output a0="P"/>
</command>
<element type="point" label="P">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="15.550559524942981" y="9.176929365675178" z="4.646514870488766"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Locus">
<input a0="P" a1="G"/>
<output a0="loc1"/>
</command>
<element type="locus" label="loc1">
<show object="true" label="false"/>
<condition showObject="m"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="12" type="15" typeHidden="1"/>
</element>
<element type="boolean" label="m">
<value val="true"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="23" y="23"/>
<labelMode val="0"/>
<caption val="顯示拋物線軌跡"/>
</element>
<element type="point" label="Q">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-15.399280027823421" y="-2.911359357478221" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="R">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-6.072153786890562" y="-2.88077861570467" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="image" label="pic1">
<file name="930442f930ffc938af1c0e8f9f298d17/image029 (1).gif"/>
<inBackground val="false"/>
<startPoint number="0" exp="Q"/>
<startPoint number="1" exp="R"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
</element>
</construction>
</geogebra>