Question

已知中心在原点,长轴在x轴上的椭圆的两准线间的距离为2根号3,若椭圆被直线x y 1截得的弦的中点的横坐...

Answer 1

a^2/c=2√3/2=√3

b^2x^2+a^2(1+x)^2-a^2b^2=0

x1+x2=-2a^2/(a^2+b^2)=-2a^2/(2a^2-c^2)=-2/(2-e^2)=-4/3

(e^2-2)=-3/2 e^2=1/2 c^2/a^2=1/2

c=√3/2,c^2=3/4

a^2=3/2 b^2=3/4

x^2/(3/2)+y^2/(3/4)=1