$A\left(5,3\right),B\left(3,-2\right),C\left(2,-1\right)$ are the points and is a point such that the area of the quadrilateral  $PABC$ is 9 sq. units then the locus of P is

$A\left(5,3\right),B\left(3,-2\right),C\left(2,-1\right),P\left(x,y\right)$
Area of Quadrilateral $PABC=9\Rightarrow \frac{1}{2}\left|\begin{array}{l}x-3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}y+2\\ 5-2\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}3+1\end{array}\right|=9$
$\Rightarrow \left|4\right(x-3)-3(y+2\left)\right|=18$
$$\begin{gathered} \Rightarrow |4x-3y-18|=18 \\ \Rightarrow 16x^2-24xy+9y^2-144x+108y=0 \end{gathered}$$