椭圆:4x^2+9y^2=36 直线m过圆x^2+y^2-4x-2y=0的圆心P,与椭圆相交A,B两点,且两点关于点P对

圆x^2+y^2-4x-2y=0 => (x-2)^2+(y-1)^2=5
圆心P=P(2,1),半径r=√5
设直线m方程为y-1=k(x-2)
设A(x1,y1),B(x2,y2)
A,B关于P对称,则x1+x2=4,y1+y2=2
将A,B代入椭圆,得
4x1^2+9y1^2=36 (1)
4x2^2+9y2^2=36 (2)
(1)-(2),=>
4(x1+x2)(x1-x2)+9(y1+y2)(y1-y2)=0
16(x1-x2)+18(y1-y2)=0
(y1-y2)/(x1-x2)=-8/9=k
∴直线方程为y=-8/9*(x-2)+1

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