L:y=√3(x+1)
a=8/2=4,c=2
b^2=4^2-2^2=12
椭圆:
x^2/16+y^2/12=1
3x^2+4y^2=48
3x^2+4[√3(x+1)]^2=48
5x^2+8x-12=0
椭圆截直线L所得的弦AB:
xA+xB=-8/5,xA*xB=-12/5
(xA-xB)^2=(xA+xB)^2-4xA*xB=(-8/5)^2-4*(-12/5)=304/25
(yA-yB)^2=[√3(xA+1)-√3(xB+1)]^2=3(xA-xB)^2
AB^2=(xA-xB)^2+(yA-yB)^2=(1+3)*304/25=1216/25
AB=8√19/5