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# Find the Equation of the Ellipse in the Following Case: Length of Major Axis 26, Foci (± 5, 0) - Mathematics

Find the equation of the ellipse in the following case:

Length of major axis 26, foci (± 5, 0)

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#### Solution

$\text{ Length of major axis }=26$
$\text{ Foci }=\left( \pm 5, 0 \right)$
$\text{ We have } 2a = 26$
$\Rightarrow a = 13$
$\text{ Also }, ae = 5$
$\Rightarrow e = \frac{5}{13}$
$\text{ Now }, e = \sqrt{1 - \frac{b^2}{a^2}}$
$\Rightarrow \frac{5}{13} = \sqrt{1 - \frac{b^2}{169}}$
$\text{ On squaring both sides, we get }:$
$\frac{25}{169} = \frac{169 - b^2}{169}$
$\Rightarrow b^2 = 144$
$\text{ Now }, \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$
$\Rightarrow \frac{x^2}{169} + \frac{y^2}{144} = 1$
$\text{ This is the required equation of the ellipse }.$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 26 Ellipse
Exercise 26.1 | Q 5.11 | Page 22
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