If the length of the major axis of the ellipse (x2)/(a2) +...

We have

$\dfrac{x2}{a2} + \dfrac{y2}{b2} = 1$

Given,

$\text{Length of the major axis} = 3 \left(\text{Length of the minor axis}\right)$

⇒ \left(2a\right) = 3 \left(2b\right)$</p><p>$⇒ a = 3b$</p><p>Now,</p><p>$e = \sqrt{1 - \dfrac{b2}{a2}}$</p><p>$⇒ e = \sqrt{1 - \dfrac{b2}{9b^{2}}}$</p><p>$⇒ e = \sqrt{1 - \dfrac{1}{9}} = \dfrac{8}{3} = \dfrac{2\sqrt{2}}{3}$</p>$