抛物线的几何构造与方程求解
2021-01-07 02:30
本范例展示抛物线的几何构造与方程求解。运用对称、垂线和轨迹等命令，动态演示抛物线作为到定点与定直线距离相等的点的轨迹生成原理。帮助学习者直观理解抛物线的定义、焦点、准线等核心概念，并推导其标准方程。
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先求出准线方程。\\
1-1 准线垂直于对称轴，且垂足是焦点关于顶点的对称点。\\
即 2T_p=F_p+P, P=2T_p-F_p=2(4,2)-(2,0)=(6,4)\\
1-2 对称轴的斜率 k_1=1, 由准线\perp对称轴，斜率之积为-1\\
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1-3 由点斜式可得 准线方程为 y=4-1\times(x-6),化成 \\
x+y-10=0\\ \\

2. 由抛物线几何定义，设抛物线上任意点M(x,y)\\
|MF_p|=Distance(M,准线)\\
(x-2)^2+(y-0)^2=\dfrac{(x+y-10)^2}{2}, 展开化简\\
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GGB https://www.geogebra.org/u/kumath""/>
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