Question

若椭圆x方/a方+y方/b方=1(a>b>0)上存在一点M,使F1M垂直F2M,求椭圆离心率范围

Answer 1

可设M(acost,bsint),(sint≠0).易知,|OM|=|c.===>(acost)^2+(bsint)^2=c^2.(因a^2=b^2+c^2)===>e=c/a=1/√[1+(sint)^2].因0√2/2≤e