# Find the Eccentricity of an Ellipse Whose Latus Rectum is Half of Its Minor Axis - Mathematics

Find the eccentricity of an ellipse whose latus rectum is  half of its minor axis

#### Solution

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

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 26 Ellipse
Exercise 26.1 | Q 9.1 | Page 23