Question

已知半圆x^2+y^2=1的直径为ab,点p在半圆上,双曲线以ab为焦点,且过点p,若

Answer 1

PA=1

PB=√3

2a=PB-PA=√3-1

a=(√3-1)/2

a^2=1-√3/2

ab为焦点,则c=1

b^2=√3/2

双曲线的方程为

x^2/(1-√3/2)-y^2/(√3/2)=1

或

y^2/(1-√3/2)-x^2/(√3/2)=1