Question

求焦点在直线2x-y=6上且离心率为2的双曲线的标准方程

Answer 1

2x-y=6,令y=0,x=3,

所以c=3,c/a=3/a=2,

a=3/2 b^2=c^2-a^2=9-9/4=27/4

双曲线为x^2/(9/4)-y^2 /(27/4)=1

或2x-y=6,令x=0,y=-6

所以c=6,6/a=2,a=3

b^2=c^2-a^2=36-9=27

双曲线为y^2/9-x^2/27=1