KEAM 2011 Math Paper

Given that, PS+PS′=8
PS=8−PS′
Squaring on both sides,
(PS)2=64+(PS′)2−16(PS′)
[∵PS=√(x+2)2+y2]
[∵PS=√(x−2)2+y2]
⇒‌‌2√x2+y2+4x+4=(x+8)
Squaring on both sides;
⇒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