设A(x1,y1),B(x2,y2),M(x0,y0)
∴ x1+x2=2x0,y1+y2=2y0
∵ A,B在椭圆x²+2y²=2
代入椭圆方程
x1²+2y1²=2 ①
x2²+2y2²=2 ②
①-②,利用平方差公式
(x1-x2)(x1+x2)+2(y1-y2)*(y1+y2)=0
∴ (x1-x2)*2x0+2(y1-y2)*2y0=0
∴ k1=(y1-y2)/(x1-x2)=-(2x0)/(4y0)=-x0/(2y0)
∵ k2=y0/x0
∴ k1*k2=-1/2(y1-y2)/(x1-x2)=-(2x0)/(4y0)这一步是怎么换算的？成比例就行了或者：(x1-x2)*2x0+2(y1-y2)*2y0=0即 4(y1-y2)*y0=-(x1-x2)*2x0 两边同时除以(x1-x2)*4y0则(y1-y2)/(x1-x2)=-(2x0)/(4y0)