# Write the Eccentricity of an Ellipse Whose Latus-rectum is One Half of the Minor Axis. - Mathematics

Write the eccentricity of an ellipse whose latus-rectum is one half of the minor axis.

#### Solution

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

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 26 Ellipse
Q 5 | Page 27