Question

分别过A（-1,0）,B（1,0）作两条互相垂直的直线,求它们的交点M的轨迹方程.

Answer 1

设M（x,y)

AM: y=k1(x+1)

BM:y=k2(x-1)

k1*k2=-1

y/(x+1)*y/(x-1)=-1

y²=-(x-1)(x+1)=-(x²-1)

x²+y²=1