# The length of the major axis of the ellipse $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}$$=1 is 2 times the length of minor axis its eccentricity is : \begin{array}{1 1}(a)\;\large\frac{\sqrt 2}{3}\\(b)\;\large\frac{\sqrt 3}{2}\\(c)\;\large\frac{\sqrt 5}{3}\\(d)\;\text{None of these}\end{array} ## 1 Answer Length of major axis =2a Length of minor axis =2b We know b^2=a^2(1-e^2) \big(\large\frac{b}{a}\big)^2$$=1-e^2$
$\big(\large\frac{1}{2}\big)^2$$=1-e^2 \large\frac{1}{4}$$-1=-e^2$
$e=\large\frac{\sqrt 3}{2}$
Hence (b) is the correct answer.
edited Sep 23, 2014