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

English

Gujarati

Hindi

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

Share

Similar Questions

If the normal at any point $P$ on the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ meets the co-ordinate axes in $G$ and $g$ respectively, then $PG:Pg = $

hard

Eccentricity of the ellipse $9{x^2} + 25{y^2} = 225$ is

easy

The acute angle between the pair of tangents drawn to the ellipse $2 x^{2}+3 y^{2}=5$ from the point $(1,3)$ is.

hard

(JEE MAIN-2022)

If the length of the latus rectum of the ellipse $x^{2}+$ $4 y^{2}+2 x+8 y-\lambda=0$ is $4$ , and $l$ is the length of its major axis, then $\lambda+l$ is equal to$……$

medium

(JEE MAIN-2022)

A rod of length $12 \,cm$ moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point $P$ on the rod, which is $3\, cm$ from the end in contact with the $x-$ axis.

hard