Given that, PS+PS′=8 PS=8−PS′ Squaring on both sides, (PS)2=64+(PS′)2−16(PS′)
{(x−2)2+y2}=64+{(x+2)2+y2}−16√(x+2)2+y2
[∵PS=√(x+2)2+y2] [∵PS=√(x−2)2+y2]
(x2+y2+4−4x)=(x2+y2+4+4x+64)−16√(x2+y2+4x+4)
⇒16√(x2+y2+4+4x)=8x+64
⇒2√x2+y2+4x+4=(x+8) Squaring on both sides;
4x2+4y2+16x+16=x2+64+16x
⇒3x2+4y2=48, which is equation of an ellipse given (y=3),∵(x,3) lies on an ellipse. ⇒3x2+4×9=48 ⇒3x2=12 ⇒x2=4 (here we take only positive value of x. ) ⇒x=±2 ⇒x=2