过P(5.4)作直线与椭圆x2/5+y2/4=1交于AB两点,则AB中点M的轨迹方程?
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![过P(5.4)作直线与椭圆x2/5+y2/4=1交于AB两点,则AB中点M的轨迹方程?](/uploads/image/z/13632565-13-5.jpg?t=%E8%BF%87P%285.4%29%E4%BD%9C%E7%9B%B4%E7%BA%BF%E4%B8%8E%E6%A4%AD%E5%9C%86x2%2F5%2By2%2F4%3D1%E4%BA%A4%E4%BA%8EAB%E4%B8%A4%E7%82%B9%2C%E5%88%99AB%E4%B8%AD%E7%82%B9M%E7%9A%84%E8%BD%A8%E8%BF%B9%E6%96%B9%E7%A8%8B%3F)
过P(5.4)作直线与椭圆x2/5+y2/4=1交于AB两点,则AB中点M的轨迹方程?
过P(5.4)作直线与椭圆x2/5+y2/4=1交于AB两点,则AB中点M的轨迹方程?
过P(5.4)作直线与椭圆x2/5+y2/4=1交于AB两点,则AB中点M的轨迹方程?
设A(x1,y1),B(x2,y2),M(x0,y0)
PAB直线方程为:y-4=k(x-5)
因AB在椭圆上:
4x1²+5y1²=20
4x2²+5y2²=20
两式相减:4(x1+x2)(x1-x2)=-5(y1+y2)(y1-y2)
4(x1+x2)/(y1+y2)=-5(y1-y2)/(x1-x2)=-5K
4x0/y0=-5K
y0-4=k(x0-5),
K=(y0-4)/(x0-5)
所以
4x0/y0=-5(y0-4)/(x0-5)
整理 4x/y=-5(y-4)/(x-5)
4x(x-5)+5(y-4)*y=0
4x²-20x+5y²-20y=0