Question

双曲线(x^2)/4-(y^2)/(b^2)=1(b∈N*)的两个焦点F1、F2,P为双曲线上一点,/OP/＜5,/PF

Answer 1

设P(x,y),c^2=4+b^2(c>0),e=c/a,

则e^2(x-4/c)(x+4/c)=4c^2 =>x^2=16+16/c^2

y^2=3b^2+4b^2/c^2

由|OP|＜5得 16+16/c^2+3b^2+4b^2/c^2