The equation of the ellipse is
x^2/a^2 + y^2/b^2 = 1.
Substitute the values of x and y in the above equation. Guess the values of a and b so that equation equals to one.
Using the relation , find the eccentricity e of the ellipse.
Co-ordinates of foci are (-ae, 0) and (ae, 0). So you can verify that F and G are fosi.
If PM' is the distance of P from the diretrix on the side of F, then
FP = e*PM' = e*(a/e + x).
Complete this part first.