
Since, the vertex of the hyperbola are A′(−2,0) and A(2,0).
Hence, the transverse axis of the hyperbola is x− axis and centre is O(0,0).
Equation of hyperbola can be taken as
a2x2−b2y2=1
⇒a=2 and ae=3
⇒e=23
Since, b2=a2(e2−1)⇒b2=a2e2−a2=9−4=5
Hence, equation of hyperbola is 4x2−5y2=1
Clearly, point (6,52) doesn't lies on the hyperbola.