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  • If the eccentricity of an ellipse is 5/8 and the distance between its foci is 10, then find latus rectum of the ellipse.

If the eccentricity of an ellipse is 5/8 and the distance between its foci is 10, then find latus rectum of the ellipse.

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Let the equation of the ellipse be \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1

Distance between foci 2ae=10

It si given that eccentricity e=\frac{5}{8}

a=\frac{10}{2}*\frac{8}{5}=8

b=\sqrt{a^{2}\left ( 1-e^{2} \right )}=\sqrt{39}

Length of latus rectum of ellipse=\frac{2b^{2}}{a}=2*\frac{39}{8}=\frac{39}{4}

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