Let an ellipse have foci at and satisfy for every point on it

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Let an ellipse have foci at

(\pm3,0)

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\sqrt{(x-3)^{2}+y^{2}}

(b)

64+12x=16\sqrt{(x-3)^{2}+y^{2}}

(c)

64-12x=16\sqrt{(x-3)^{2}+y^{2}}

(d)

64-6x=16\sqrt{(x-3)^{2}+y^{2}}