双曲线的基本描点与几何构造
2013-06-11 12:35
本范例演示了双曲线的基本描点方法与几何构造过程。通过利用点、线段、圆、中垂线及对称等基础几何元素与命令，逐步构造出双曲线上的关键点。该过程直观地展示了双曲线的几何性质及其轨迹特征，有助于深入理解圆锥曲线的定义与作图原理。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="4.2" version="4.2.36.0" id="4c5c9c58-f3e2-4a56-9a64-f684278a7f04" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="800" height="600" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.25" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1" size="400" window="370,145,700,550" />
<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 || 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="576" window="100,100,600,400" />
<view id="2" visible="true" inframe="false" stylebar="false" location="3" size="200" 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" 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" position="1" help="false" />
<input show="true" cmd="true" top="false" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="12"/>
<graphicsSettings javaLatexFonts="false"/>
</gui>
<euclidianView>
<size width="576" height="413"/>
<coordSystem xZero="120.96054545454555" yZero="172.9164659090909" scale="53.87215909090913" yscale="53.87215909090907"/>
<evSettings axes="false" grid="true" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="13" 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" tickDistance="1.0"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true" tickDistance="1.0"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
<startAnimation val="true"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="d">
<value val="2.2"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="10" absoluteScreenLocation="true" width="300.0" x="247.0" y="69.0" fixed="true" horizontal="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<element type="point" label="A">
<show object="true" 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="1.0" y="-1.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="B">
<show object="true" 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="5.0" y="-1.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Line">
<input a0="A" a1="B"/>
<output a0="b"/>
</command>
<element type="line" label="b">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="4.0" z="4.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Point">
<input a0="b"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="true" 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="true"/>
<coords x="-145.26548672595996" y="-1.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="A" a1="C"/>
<output a0="c"/>
</command>
<element type="segment" label="c">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-146.26548672595996" z="-146.26548672595996"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Circle">
<input a0="A" a1="C"/>
<output a0="e"/>
</command>
<element type="conic" label="e">
<show object="true" label="false"/>
<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="-21391.59260718197" A3="0.0" A4="-1.0" A5="1.0"/>
<eqnStyle style="specific"/>
</element>
<command name="Circle">
<input a0="B" a1="c + d"/>
<output a0="f"/>
</command>
<element type="conic" label="f">
<show object="true" label="false"/>
<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="-22016.00074877619" A3="0.0" A4="-5.0" A5="1.0"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="e" a1="f"/>
<output a0="D" a1="E" a2="" a3=""/>
</command>
<element type="point" label="D">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<trace val="true"/>
<coords x="-78.05101769927751" y="122.06311067046244" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="E">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<trace val="true"/>
<coords x="-78.05101769927751" y="-124.06311067046244" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="LineBisector">
<input a0="B" a1="A"/>
<output a0="a"/>
</command>
<element type="line" label="a">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4.0" y="0.0" z="-12.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="LineBisector">
<input a0="D" a1="E"/>
<output a0="g"/>
</command>
<element type="line" label="g">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="246.12622134092487" z="246.12622134092487"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Mirror">
<input a0="E" a1="a"/>
<output a0="E'"/>
</command>
<element type="point" label="E'">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<trace val="true"/>
<coords x="84.05101769927752" y="-124.06311067046242" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Mirror">
<input a0="D" a1="a"/>
<output a0="D'"/>
</command>
<element type="point" label="D'">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<trace val="true"/>
<coords x="84.0510176992775" y="122.06311067046245" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
</construction>
</geogebra>