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  • If the latus rectum of an ellipse is equal to half of minor axis, then find its eccentricity.

If the latus rectum of an ellipse is equal to half of minor axis, then find its eccentricity.

Answers (1)

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

It is given that length of latus rectum = Half of minor axis

\frac{2b^{2}}{a}=b

a=2b

b2=a2(1-e2)

b2=4b2(1-e2)

1-e2=1/4

e2=3/4

e=\frac{\sqrt{3}}{2}

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infoexpert22

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