The correct option is B 7
Given hyperbola is, x2144−y281=125
⇒x2144/25−y281/25=1
⇒a2=14425,b2=8125,e=√1+b2a2=√1+81144=1512
∴ foci of hyperbola are (±ae,0)i.e(±3,0)
Now given ellipse is x216+y2b2=1
⇒a2=16
Assume eccentricity of this ellipse is e′ then its foci are (±ae′,0)i.e(±4e′,0)
Given focci of given hyperbola and ellipse coincide
⇒4e′=3⇒e′=34
For ellipse, using eccentricity relationship, e′2=1−b2a2
⇒916=1−b216
∴b2=7