Question

数学圆锥曲线与圆X^2＋Y^2﹣X＋2Y=0关于直线：X﹣Y+1=0对称的圆的方程为?

Answer 1

圆x^+y^-x+2y=0,即(x-1/2)^+(y+1)^=5/4,

设圆心A(1/2,-1)关于直线l:x-y+1=0的对称点为A'(x,y),则

l垂直平分AA',

∴（y+1)/(x-1/2)=-1,

(1/2+x)/2-(y-1)/2+1=0,

化简得y=-x-1/2,

x-y+7/2=0,

解得x=-2,y=3/2.

∴圆A':(x+2)^+(y-3/2)^=5/4,为所求.