The line x+y+2=0 intersect the circle x^2+y^2+4 x-4 y-4=0 in two points A and B . Let S x^2+y^2+2 g x+2 fy + c =0 be a different circle passing through the points A and B . If the distance of the centre of S=0 from A B is 2 , then g + f + c =

Step-by-step solution

Equation of circle(s) passing through intersection of line and circle is x^2+y^2+4 x-4 y-4+ (x+y+2)=0x^2+y^2+(4+ ) x+( -4) y+(2 -4)=0 But x^2+y^2+2 g x+2 f y+c=0 (Given) g= 4+ 2 , f= -4 2 , c=2 -4 Given that distance of (-g,-f) from x+y+z=0 is 2 aligned & | -g-f+2 2 |= 2 g+f=4 & 4+ 2 + -4 2 =4 =4 g=4, f=0, c=4 & Now, g+f+c=4+0+4=8 aligned