The inverse of the point (1,2) with respect to the circle x^2+y^2-4 x-6 y+9=0 , is

Step-by-step solution

The equation of pole w.r.t. the point (1,2) to the circle x^2+y^2-4 x-6 y+9=0 is aligned x+2 y-2(x+1)-3(y+2)+9 & =0 x+y-1 & =0 aligned x+y-1=0 foot ( , ) of the perpendicular from the point (1,2) to the line x+y-1 . aligned & & -1 1 = -2 1 & =- (1 1+1 2-1) 1^2+1^2 & & -1 & = -2=-1 & & & =0, =1 aligned Hence, required point is (0,1) .