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 :
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Official solution
\[{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\] meets the line \[{x \over 7} + {y \over {2\sqrt 6 }} = 1\] on the x-axis
So, a=7
and \[{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\] meets the line \[{x \over 7} - {y \over {2\sqrt 6 }} = 1\] on the y-axis
So, \[b = 2\sqrt 6 \]
Therefore, \[{e^2} = 1 - {{{b^2}} \over {{a^2}}} = 1 - {{24} \over {49}}\]
\[e = {5 \over 7}\]