If `A(-1,1)a n d\ B(2,3)` are two fixed points, find the locus of a point `P` so that the area of ` Delta P A B=8s qdot` units.

Explanation

Let the point `P(x_1, y_1)`.
Given area (formed by these points) of the triangle `APB = 8 ⇒ frac{1}{2}[x_1(y_2 – y_3) + x_2(y_3 – y_1) + x_3(y_1 – y_2)] = 8`

` ⇒ frac{1}{ 2} [x_1(1 – 3) + (-1) (3 – y_1) + 2(y_1 – 1)] = 8`
`⇒ frac{1 }{2}[-2x_1 – 3 + y_1 + 2y_1 – 2] = 8`

`frac{1 }{2} [-2x_1 + 3y_1 – 5] = 8 ⇒ -2x_1 + 3y_1 – 5 = 16`

`⇒ -2x_1 + 3y_1 – 21 = 0`

`⇒ 2x_1 – 3y_1 + 21 = 0`