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# Find the length of major and minor axes of the ellipse $3x^2+2y^2=6$?Also find its eccentricity?

$\begin{array}{1 1}(a)\;\text{Length of major axes }=2\sqrt{5},\text{Length of minor axes }=2\sqrt{7},e=\large\frac{1}{\sqrt 5}\\(b)\;\text{Length of major axes }=2\sqrt{3},\text{Length of minor axes }=2\sqrt{2},e=\large\frac{1}{\sqrt 3}\\(c)\;\text{Length of major axes }=\sqrt{5},\text{Length of minor axes }=\sqrt{2},e=\large\frac{1}{\sqrt 7}\\(d)\;\text{Length of major axes }=2\sqrt{8},\text{Length of minor axes }=2\sqrt{3},e=\large\frac{1}{\sqrt 8}\end{array}$

$\large\frac{x^2}{2}+\frac{y^2}{3}$$=1 \large\frac{x^2}{\sqrt{2^2}}+\frac{y^2}{\sqrt{3^2}}$$=1$
$a=\sqrt 2,b=\sqrt 3$
Length of major axes =2b=$2\sqrt 3$
Length of minor axes =2a=$2\sqrt 2$
$a^2=b^2(1-e^2)$
$2=3(1-e^2)$
$e^2=\large\frac{1}{3}$
$e=\large\frac{1}{\sqrt 3}$
Hence (b) is the correct answer.