Question

`A(5,3), B(3,-2)` are two fixed points; find the equation to the locus of a point `P` which moves so that the area of the triangle `P A B` is 9 units.

Answer 1

area of triangle`=1/2|[x_!,y_1,1],[x_2,y_2,1],[x_3,y_3,1]|`
`/_=1/2|[h,k,1],[5,3,1],[3,-2,1]|=9`
`/_=h(3+2)-k(5-3)+1(-10-9)=18`
`5h-2k-19=18`
`5h-2k=37`
putting h=x,k=y
`5x-2y=37`.