The correct option is B x216−y29=−1
We have e1=√1−1625=35
∵e1e2=1⇒e2=53
Clearly y-axis is transverse axis of the ellipse.
Thus, coordinates of focii of the ellipse are (0,±be1) or (0,±3).
Let hyperbola is, y2b2−x2a2=1..(1)
given hyperbola passes through foci of the ellipse
⇒b2=9 and also a2=b2(e2−1)=9(25/9−1)=16
Therefore, required hyperbola is, x216−y29=−1
Hence, option 'A' is correct.