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Find the Equation of the Ellipse in the Following Case: Foci (± 3, 0), a = 4 - Mathematics

Find the equation of the ellipse in the following case:

Foci (± 3, 0), a = 4

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Solution

$\text{ Foci }=\left( \pm 3, 0 \right)\text{ and }a=4$
$\text{ i . e } . ae = 3$
$\Rightarrow e = \frac{3}{4}$
$\text{ Now }, e = \sqrt{1 - \frac{b^2}{a^2}}$
$\Rightarrow \frac{3}{4} = \sqrt{1 - \frac{b^2}{16}}$
$\text{ On squaring both sides, we get }:$
$\frac{9}{16} = \frac{16 - b^2}{16}$
$\Rightarrow b^2 = 7$
$\therefore \frac{x^2}{16} + \frac{y^2}{7} = 1$
$\text{ This is the required equation of the ellipse }.$

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 26 Ellipse
Exercise 26.1 | Q 5.13 | Page 22
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