Doubts about locus and its equation Two points A and B with $(1,1)$ and $(-2,3)$ respectively are given.find the locus of point P.So that area of $\Delta$PAB is 9 square units.
answer is :- $2x+3y+13=0$ or  $2x+3y-23=0$.
how i tried:-
i assigned unknown point to be P$(x,y)$ and completed the triangle and from point P i drew a perpendicular until point O(a random point on line-segment AB).  

 i found point O in terms of $x_1$ and $y_1$ using equation of line.Now perpendicular line PO is height and the base is AB. Now i used formula $\dfrac{1}{2}(base *height)$.On equating the following this equation with 9, i ended up with the wrong answer.please can someone help me find the solution?? please.

Assuming  $P(h,k),$ 
I found $$\frac12\cdot\sqrt{13}\cdot\frac{|2h+3k-5|}{\sqrt{13}}=9\iff|2h+3k-5|=18$$
which complies with the given answer
