If the circle x^2+y^2+2 g x+2 f y+c=0(c>0) touches both the coordinate axes and lies in the third quadrant, then the length of the chord intercepted by the circle on the line x+y+ c =0 is

Step-by-step solution

Given equation of circle x^2+y^2+2 g x+2 f y+c=0 (c>0) Coordinate of centre =(-g,-f) radius = g^2+f^2-c Circle touch both the axes, so aligned g^2 & =f^2=c g= c f & = c aligned So, coordinate of centre lies in third quadrant so, centre is (- c ,- c ) equation of given line x+y+ c =0 So, line pass through the point of contact to axes of the circle. Hence, intercept aligned A B & = (- c -0)^2+(0+ c )^2 & = c+c = 2 c aligned