Question

求以椭圆x的平方/16+y的平方/9=1的定点为焦点,且有一条渐近线x+2y=0的双曲线方程

Answer 1

顶点(±4,0)或(0,±3)

1.(±4,0)为焦点,c=4,a:b=2:1 c^2=a^2+b2,焦点在x轴,a^2=64/5,b^2=16/5

x^2/(64/5)-y^2/(16/5)=1

2.(0,±3)为焦点,c=4,a:b=1:2 焦y轴,a^2=64/5,b^2=16/5

y^2/(64/5)-x^2/(16/5)=1