I didn't know which forum to put it in, but I thought this was the most appropriate.

This is the question:

Given two points A(3,-2) and B(-1,7), find the equation of the locus of P(x,y) if the gradient of PA is twice the gradient of PB.

I've tried it 2 different ways and keep getting the same solution:

xy + 5y + 11x - 17 = 0

However the answer in the book says otherwise...

Working:

$\displaystyle PA' = \frac{y+2}{x-3}$

$\displaystyle PB' = \frac{y-7}{x+1}$

$\displaystyle 2 PA' = PB'$

$\displaystyle \frac{2y+4}{x-3} = \frac{y-7}{x+1}$

...

$\displaystyle xy + 5y + 11x -17 = 0$