Question

已知双曲线x^2/a^2-y^2/b^2=1过右焦点F作一条渐近线的垂线与双曲线交于M垂足为N

Answer 1

设F（c,0) 渐近线y=b/ax

过F的直线y=-a/b(x-c)

连列两线,计算得x=a^2/c

代入得y=ab/c

N(a^2/c,ab/c)

M(1/2(c+a^2/c), 1/2*ab/c)

M坐标代入抛物线方程,c^2/a^2=2

e=c/a=根号2