I think you have your 'twice' on the wrong side.
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...