Question

已知椭圆x²/a²+y²/b²=1(a>b>0)与双曲线x²/m&su

Answer 1

对椭圆：c^2=a^2-b^2

对双曲线:c^2=m^2+n^2

若c是a、m的等比中项,则c^2=am

n²是2m²与c²的等差中项.,则2n^2=2m^2-c^2

e^2=(c/a)^2=m^2/c^2=m^2/(m^2+n^2)=3n^2/(3n^2+n^2)=3/4

因e>0,所以e=√3/2