# If the Latus Rectum of an Ellipse is One Half of Its Minor Axis, Then Its Eccentricity is - Mathematics

MCQ
Sum

If the latus rectum of an ellipse is one half of its minor axis, then its eccentricity is

#### Options

• $\frac{1}{2}$

• $\frac{1}{\sqrt{2}}$

• $\frac{\sqrt{3}}{2}$

• $\frac{\sqrt{3}}{4}$

#### Solution

$\frac{\sqrt{3}}{2}$
According to the question, the latus rectum of an ellipse is half its minor axis.
$i . e . \frac{2 b^2}{a} = \frac{1}{2} \times 2b$
$\Rightarrow 2 b^2 = ab$
$\Rightarrow a = 2b$
$\text{ Now, }e = \sqrt{1 - \frac{b^2}{a^2}}$
$\Rightarrow e = \sqrt{1 - \frac{b^2}{4 b^2}}$
$\Rightarrow e = \sqrt{1 - \frac{1}{4}}$
$\Rightarrow e = \sqrt{\frac{3}{4}}$
$\Rightarrow e = \frac{\sqrt{3}}{2}$

Concept: Introduction of Ellipse
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 26 Ellipse
Q 15 | Page 29