Question

椭圆x^/3m^+y^/5n^=1和双曲线x^/2m^-y^/3n^=1有公共焦点,双曲线的渐进方程是

Answer 1

焦点在X轴上,设焦点F1（-c,0),F2(c,0),

3m^2-5n^2=2m^2+3n^2,

m^2=8n^2,

m=2√2n,

双曲线方程为：x^2/(4n)^2-y^2/(√3n)^2=1,

渐近线方程：y=±√3x/4.