Question

点M是在椭圆x^2/a^2=y^2/b^2=1上,以M为圆心的圆与X轴相切于椭圆的右焦点

Answer 1

(1)椭圆经过(c,c)点.c^2/a^2+c^2/b^2=1,c^2/a^2+c^2/(a^2-c^2)=1,e^2=(3-√5)/2,e=(√5-1)/2

(2)由三角形ABM是边长为2的正三角形,c=√3,由离心率,a^2=3(3+√5)/2,椭圆方程为x^2/[3(3+√5)/2]+y^2/[3(1+√5)/2]=1.