The equation of the circle passing through the points of intersection of the circles x^2+y^2+4 x+6 y-12=0 and x^2+y^2-6 x-4 y-12=0 and cutting the circle x^2+y^2-4 x+4 y+8=0 orthogonally is

Step-by-step solution

Equation of the circle passing through the points of intersection of the circles and aligned x^2+y^2+4 x+6 y-12 & =0 x^2+y^2-6 x-4 y-12 & =0 aligned and is (x^2+y^2+4 x+6 y-12 ) array r + (x^2+y^2-6 x-4 y-12 )=0 x^2+y^2+ 4-6 1+ x+ 6-4 1+ -12=0 (iii) array Since, the another circle x^2+y^2-4 x+2 y+8=0 cuts the circle (iii) orthogonally, then aligned & -2 ( 4-6 1+ )+ ( 6-4 1+ )=8-12=-4 & -8+12 +6-4 =-4-4 & 12 =-2 =- 1 6 aligned So, required equation of circle is aligned & 6 (x^2+y^2+4 x+6 y-12 ) & - (x^2+y^2-6 x-4 y-