AP EAMCET Engineering 2018 Apr 24 Shift 1 Paper

The circle's equation is
x2+y2+2gx+2fy+c=0
Coordinate of centre =(−g,−f)
radius =√g2+f2−c since circle touches both the axes
g2=f2
g=±√c
Therefore, the coordinate of the centre (−√c,−√c)
The equation of the given line is
x+y+√c=0
Therefore, intercept
AB=√(−√c−0)2+(0+√c)2 =√2c