The length of the semi-latus rectum of an ellipse is one thrid of its major axis, its eccentricity would be

Question

The length of the semi-latus rectum of an ellipse is one thrid of its major axis, its eccentricity would be (A) (2/3) (B) √(2/3) (C) (1/√3) (D) (1/√2)

Tardigrade Admin · Accepted Answer

As per the question (2 b2/a)=(1/3)(2 a) (b2/a2)=(1/3) Eccentricity is given as e 2 =1-( b 2/ a 2) =1-(1/3) =(2/3)

Q. The length of the semi-latus rectum of an ellipse is one thrid of its major axis, its eccentricity would be

$\frac{2}{3}$

$\frac{2}{3}$

$\frac{1}{3}$

$\frac{1}{2}$

As per the question
$\frac{2 b ^{2}}{a} = \frac{1}{3} (2 a)$
$\frac{b ^{2}}{a ^{2}} = \frac{1}{3}$
Eccentricity is given as
$e^{2} = 1 - \frac{b ^{2}}{a ^{2}}$
$= 1 - \frac{1}{3}$
$= \frac{2}{3}$

Q. The length of the semi-latus rectum of an ellipse is one thrid of its major axis, its eccentricity would be

32​

32​​

3​1​

2​1​

As per the question a2b2​=31​(2a) a2b2​=31​ Eccentricity is given as e2=1−a2b2​ =1−31​ =32​

$\frac{2}{3}$

$\frac{2}{3}$

$\frac{1}{3}$

$\frac{1}{2}$

As per the question
$\frac{2 b ^{2}}{a} = \frac{1}{3} (2 a)$
$\frac{b ^{2}}{a ^{2}} = \frac{1}{3}$
Eccentricity is given as
$e^{2} = 1 - \frac{b ^{2}}{a ^{2}}$
$= 1 - \frac{1}{3}$
$= \frac{2}{3}$