If P is a point on the rectangular hyperbola x2−y2=a2, C is its centre and S, and S′ are the two foci, then SP.S′P=
2
(CP)2
(CS)2
(SS′)2
PS=ex+a=√2x+a
PS′=ex−a=√2x−a [Here, e is eccentricity]
PS×PS′=2x2−a2
=2x2−(x2−y2)
=x2+y2=(CP)2
If P is a point on the rectangular hyperbola x2−y2=a2, C is its centre and S,S′ are the two foci, the SP⋅S′P=