Answer:
Option C
Explanation:
Concept involved equation of an ellipse is
x2a2+y2b2=1 (a >b)
Ecentricity e2=1−b2a2 (a >b)

Description of Situation As ellipse circumscribes the rectangle, then it must
pass through all four vertices.
Sol. Let the equation of Ellipse E2 be
x2a2+y2b2=1 , where a<b and b=4

Also, it passes through (3,2)
⇒ 9a2+4b2=1 (∵ b=4)
⇒ 9a2+14=1 or a2=12
Eccentricity of E2
⇒ e2=1−a2b2=1−1216=14 (∵ a <b)
∴ e=12