椭圆为x2/4+y2/3=1,直线和椭圆交于A,B两点,求过三点A,B,F的圆的方程

椭圆为x2/4+y2/3=1,直线和椭圆交于A,B两点,求过三点A,B,F的圆的方程

x^2/4+y^2/3=1
c=1
F(1,0)
y=kx+m
x^2+4(kx+m)^2=12
(1+4k^2)x^2+8kmx+4m^2-12=0
xA+xB=-8km/(1+4k^2),xA*xB=(4m^2-12)/(1+4k^2)
(xA-xB)^2=(xA+xB)^2-4xA*xB=
(yA-yB)^2=k^2*(xA-xB)^2
AB^2=(xA-xB)^2+(yA-yB)^2=(1+k^2)*(xA-xB)^2=
(AB/2)^2=AB^2/4=
AB的中点P
xP=(xA+xB)/2=-4km/(1+4k^2)
yP=k*xP+m
过P垂直AB的直线：y-yP=(-1/k)*(x-xP)
x=a,y=( )a
圆心C(a,b)
圆心C 到直线AB的距离d
d=
d^2+(AB/2)^2=r^2=CF^2
a=,b=,r^2=
C:(x-a)^2+(y-b)^2=r^2