The centre of a circle which cuts x²+y²+6 x-1=0, x²+y²-3 y+2=0 and x²+y²+x+y-3=0 orthogonally is

Step-by-step solution

The given circles Let S₁=x²+y²+6 x-1=0 , Centre C₁=(-3,0) , Radius R₁= 10 S₂ x²+y²-3 y+2=0, gathered C₂=(0,3 / 2), R₂=1 / 2 S₃ x²+y²+x+y-3-0, C₃=(-1 / 2,-1 / 2), R₃= 7 / 2 gathered Let S=x²+y²+2 g x+2 f y+c=0 be equation of circle which cut orthogonal all three circles. Then, by condition of orthogonality g+f=c-3 On solving Eqs. (i), (ii) and (iii), we get g=1 / 7, f=-9 / 7 So, centre is (-g,-f)=(-1 / 7,9 / 7)