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)
\Rightarrow \frac{9}{a^{2}}+\frac{1}{4}=1 or a^{2}=12
Eccentricity of E_{2}
\Rightarrow e^{2}=1-\frac{a^{2}}{b^{2}}=1-\frac{12}{16}=\frac{1}{4} ( \because a <b)
\therefore e=\frac{1}{2}