Discussion Forum

If A=[5,3], B=[3,-2] and a point P is such that the area of the triangle PAB is 9, then the locus of P  represents.

Answer:

Explanation:

Let P(x,y), A=(5,3),B=(3,-2)

Area of $\triangle PAB$= $\frac{1}{2}\begin{bmatrix}x & y&1 \\5 & 3&1\\3&-2&1 \end{bmatrix}$

$\Rightarrow$              $9=\frac{1}{2}|x(3+2)-y(5-3)+(-10-9)|$

$\Rightarrow$     $18=|5x-2y-19|$

$\Rightarrow$   $5x-2y-16=|18|$

$\Rightarrow$     $5x-2y-19=\pm18$

$\Rightarrow$   $5x-2y=19 \pm 18$

$\Rightarrow$     $5x-2y=1  $ or $5x-2y=37$

Which represents a pair of parallel lines