If the lines $2x-3y=5$ and $3x-4y=7$ are the diameters of a circle of area 154 square units,then obtain the equation of the circle.

Question

$\begin{array}{1 1}x^2+y^2+2x+2y-47=0\\x^2+y^2-2x-2y-47=0\\x^2+y^2-2x+2y-47=0\\x^2+y^2+2x-2y-47=0\end{array}$