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  • If the ellipse  <img alt="\mathrm{\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1}" src="/latex-image/?%5Cmathrm%7B%5Cfrac%7Bx%5E%7B2%7D%7D%7Ba%5E%7B2%7D%7D&plus;%5Cfrac%7By%5E%7B2%7D%7D%7Bb%5E%

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

 

Option: 1

\frac{5}{7}


Option: 2

\frac{2 \sqrt{6}}{7}


Option: 3

\frac{3}{7}


Option: 4

\frac{2 \sqrt{5}}{7}


Answers (1)

best_answer

Line 1 and ellipse cut x-axis at \mathrm{x=7} and line 2 and ellipse cut y-axis at \mathrm{y=2\sqrt{6}}

\mathrm{\therefore \quad a=7, \quad b=2 \sqrt{6}} \\

\mathrm{e^{2}=1-\frac{b^{2}}{a^{2}}=1-\frac{24}{49}=\frac{25}{49}} \\

\mathrm{\Rightarrow e=\frac{5}{7}}

Hence correct option is 1

Posted by

manish painkra

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