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Question

If the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ meets the line $\frac{x}{7}+\frac{y}{2 \sqrt{6}}=1$ on the $x$-axis and the line $\frac{x}{7}-\frac{y}{2 \sqrt{6}}=1$ on the $y$-axis, then the eccentricity of the ellipse is :

$\frac{5}{7}$
$\frac{2 \sqrt{6}}{7}$
$\frac{3}{7}$
$\frac{2 \sqrt{5}}{7}$

Solution

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