Question

若椭圆x^2/k+8+y^2/9=1的离心率=1/2,求k

Answer 1

1# 焦点在x轴上 ;c^2 = k+8-9 = k-1; a^2 = k+8

e^2=1/4 = (k-1)/(k+8);

k+8 = 4k-4,所以 k=4; x^2/12+y^2/9=1

2# 焦点y 轴上,c^2=9-8-k=1-k

e^2=1/4 = (1-k)/9 4-4k=9;k= -5/4