Find the locus of the point P(x,y) such that the area of the triangle PAB is 5, where A is the point (1,-1) and B is the point (5,2).

Explanation

`therefore` Area of the triangle PAB is
1/2{x(-1-2) + 1(2-y) + 5(y+1)}
= 1/2 (-3x+2-y+5y+5)
1/2(-3x+4y+7)
= 1/2 (-3x+4y+7) = 5
or, -3x+4y+7 = 10
or, 3x-4y+3 = 0
which is the locus of the point P(x,y).