A(5, 3), B(3,-2), C(2, -1) are the points and P is a point such that the area of the quadrilateral PABC is 10 square units then the locus of P is 

Let P = (x, y), A = (5, 3) B(3, -2) C(2, -1) Area of quadrilateral PABC = 10

$\Rightarrow \left|\text{4x\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}\hspace{0.17em}3y\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}\hspace{0.17em}18\hspace{0.17em}\hspace{0.17em}}\right|=20$

$\Rightarrow \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}4x\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}\hspace{0.17em}3y\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}\hspace{0.17em}18\hspace{0.17em}\hspace{0.17em}=\hspace{0.17em}}\pm \text{\hspace{0.17em}20}$

Locus of P is $\left(\text{4x-3y-38}\right)\left(\text{4x-3y+2}\right)\text{\hspace{0.17em}=\hspace{0.17em}0}$