Question

设动直线l垂直于x轴,且与椭圆x²﹢2y²＝4交于Α、Β两点,Ρ是l上满足向量ΡΑ乘以向量ΡΒ等

Answer 1

设P点坐标为(x,y),则A(x,a),B(x,-a)

x^2+2*a^2=4,a=根号[(4-x^2)/2]

A(x,根号[(4-x^2)/2]),B(x,-根号[(4-x^2)/2])

向量PA乘向量PB=(0,a-y)乘(0,-a-y)=y^2-a^2=1

化简得：x^2+2y^2=6