The correct option is A x2+y2−6y−7=0
Equation of the ellipse is
x216+y29=1⇒a=4, b=3e=√1−b2a2⇒e=√1−916⇒e=√74
Foci are (±ae,0)≡(±√7,0)
Equation of circle with centre (0,3) and radius r is
x2+(y−3)2=r2 ⋯(1)
This circle passes throught (√7,0)
⇒(√7)2+(0−3)2=r2⇒r2=16
Now, from equation (1)
x2+(y−3)2=16⇒x2+y2−6y−7=0