Question

If the circle $x^2+y^2+2gx+2fy+c=0$ is touched by $y=x$ at P such that $OP=6\sqrt{2}$ then value of C is

• A. 36
• B. 144
• C. 72
• D. none of these

Answer 1

The correct option is C 72

In triangle OCP ,using Pythagoras theorem

cp=radius=$g^2+f^2-c$

$O{C}^2=C{P}^2+O{P}^2⟹g^2+f^2=72+g^2+f^2-c$

$⟹c=72$