Let the equation of the required ellipse be $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}$$=1$
As it passses through $(-3,1)$ we get,
$\large\frac{9}{a^2}+\frac{1}{b^2}$$=2$
=> $9b^2+a^2=a^2b^2$
=> $9a^2(1-e^2)+a^2=a^2.a^2(1-e^2)$
=> $9a^2(1- \large\frac{2}{5})$$+a^2=a^4(1- \large\frac{2}{5})$
=> $a^2=\large\frac{32}{5}$
Now $b^2=a^2(1-e^2)$
=> $b^2=\large\frac{32}{3} (1-\large\frac{2}{5})$
$\qquad= \large\frac{32}{5}$
Hence the equation of required ellipse is
$\large\frac{x^2}{\Large\frac{32}{3}}+\frac{y^2}{\Large\frac{32}{5}}$$=1$
(or) $3x^2+5y^2=32$
Hence C is the correct answer.