双曲线x^2/a^2+y^2/b^2=1的左右焦点为F1,F2.线段F1F2被抛物线y^2=2bx的焦点分成7:5两段则双曲线离心率

题目

双曲线x^2/a^2+y^2/b^2=1的左右焦点为F1,F2.线段F1F2被抛物线y^2=2bx的焦点分成7:5两段则双曲线离心率

答案

抛物线y^2=2bx,的焦点坐标是F(b/2,0)F1F2被F分成了7:5的二段,则有F1F/FF2=7/5,即有(b/2+c)/(c-b/2)=7/5即有7(c-b/2)=5(c+b/2)7c-7b/2=5c+5b/22c=6bc=3bc^2=a^2+b^2c^2=a^2+c^2/9a^2=8/9c^2e^2=c^2/a^2=9/8e=3/4*根号...