Length of latus rectum of an ellipse is frac{1}{3} of major axis. Its eccentricity is

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10-2. Parabola, Ellipse, Hyperbola

easy

The length of the latus rectum of an ellipse is $\frac{1}{3}$ of the major axis. Its eccentricity is

A

$\frac{2}{3}$

B

$\sqrt {\frac{2}{3}} $

C

$\frac{{5 \times 4 \times 3}}{{{7^3}}}$

D

${\left( {\frac{3}{4}} \right)^4}$

Solution

(b) Latus rectum $ = 1/3$ (Major axis)

==> $\frac{{2{b^2}}}{a} = \frac{{2a}}{3}$

==> ${a^2} = 3{b^2} = 3{a^2}(1 – {e^2})$

==> $e = \sqrt {\frac{2}{3}} $.

Standard 11

Mathematics

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