Question

已知椭圆x2/4+y2/3=1的长轴端点MN,异于MN的点P在椭圆上,求Kpm*Kpn

Answer 1

设椭圆上的点P(x,y),则y²=3(1-x²/4)=(3/4)(4-x²),

∵M(-2,0),N(2,0),

∴Kpm=y/(x+2),Kpn=y/(x-2),

∴Kpm·Kpn=y²/(x²-4)=(3/4)(4-x²)/(x²-4)=-3/4.