Let an ellipse have foci at (±3,0) and satisfy PA+PB=8 for every point P(x,y) on it. After squaring the defining relation once, which of the following equations is obtained (radicals not yet fully eliminated)?
a) 64−12x=8(x−3)2+y2
b) 64+12x=16(x−3)2+y2
c) 64−12x=16(x−3)2+y2
d) 64−6x=16(x−3)2+y2