Ans: C
Let $(x,y)$ be the coordinates of $P$. Then the equation of the locus of $P$ is
$\begin{array}{rcl}
PM & = & MN \\
\sqrt{(x-5)^2 +(y-7)^2} & = & \sqrt{6-5)^2 +(8-7)^2} \\
x^2 -10x +25 +y^2 -14y+49 & = & 2 \\
x^2 +y^2 -10x -14y +72 & = & 0
\end{array}$
