过椭圆x^2/4+y^2/3=1得右焦点做倾角为45度的弦AB,求以AB为直径的圆的方程

x^2/4+y^2/3=1
右焦点C=√(a^2-b^2)=1
AB:y=x-1
x^2/4+(x-1)^/3=1
(3x^2+4x^2-8x+4)=12
7x^2-8x-8=0
这个圆圆心（(x1+x2)/2,(y1+y2)/2）
(x1+x2)/2=4/7
(y1+y2)/2=((x1-1)+(x2-1))/2=-3/7
直径长√((y2-y1)^2+(x2-x1)^2)
(y2-y1)^2=(y2+y1)^2-4y1y2
=(x1-1+x2-1)^2-4*(x1-1)(x2-1)
=(x1+x2-2)^2-4x1x2+4(x1+x2)-4
=(36/49)+4*8/7+4*8/7-4
=(36+36*7)/49
=288/49
(x2-x1)^2=(x1+x2)^2-4x1x2
=64/49+4*8/7
=(64+32*7)/49
=288/49
√((y2-y1)^2+(x2-x1)^2)=√(576/49)=24/7
半径=12/7
这个圆是
(x-4/7)^2+(y+3/7)^2=144/49