The locus of P such that area of $△PAB$ is 12 sq.units.Where $A=\left(2,3\right)$  and $B=\left(-4,5\right)$

Let $P=\left(x,y\right).$ Given that area of $\Delta PAB=12squnits$
$\begin{array}{l}\Rightarrow \frac{1}{2}\left|\begin{array}{cc}2+4& 3-5\\ 2-x& 3-y\end{array}\right|=12\Rightarrow \left|\begin{array}{cc}6& -2\\ (2-x)& (3-y)\end{array}\right|=24\Rightarrow \left|6\right(3-y)-(-2\left)\right(2-x\left)\right|=24\\ \Rightarrow |22-6y-2x|=24\Rightarrow |-2(x+3y-11\left)\right|=24\Rightarrow |-(x+3y-11\left)\right|=12\Rightarrow (x+3y-11{)}^2=144\\ \Rightarrow x^2+6xy+9y^2-22x-66y-23=0\end{array}$