Question

关于双曲线的渐近线方程已知椭圆x²/3m²+y²/5n²和双曲线x²/

Answer 1

椭圆a^2=3m^2,b^2=5n^2

c^2=3m^2-5n^2

双曲线a^2=2m^2,b^2=3n^2

c^2=2m^2+3n^2

有公共焦点

所以3m^2-5n^2=2m^2+3n^2

m^2=8n^2

n^2/m^2=1/8

n/m=√2/4

渐近线方程y=±b/ax

=±√(3n^2/2m^2)x=±√(3/16)x=±√3/4x

即y=±[(√3)/4]x