# Find the Equation of the Ellipse in the Following Case: Length of Minor Axis 16 Foci (0, ± 6) - Mathematics

Find the equation of the ellipse in the following case:

Length of minor axis 16 foci (0, ± 6)

#### Solution

$\text{ Length of minor axis }=16 \text{ and foci }=\left( 0, \pm 6 \right)$
$\text{ i . e } . 2b = 16$
$\Rightarrow b = 8$
$\text{ and }$
$\text{ be } = 6$
$\Rightarrow e = \frac{6}{8}$
$\text{ Now }, e = \sqrt{1 - \frac{a^2}{b^2}}$
$\Rightarrow \frac{6}{8} = \sqrt{1 - \frac{a^2}{64}}$
$\text{ On squaring both sides, we get }:$
$\frac{36}{64} = \frac{64 - a^2}{64}$
$\Rightarrow a^2 = 28$
$\frac{x^2}{64} + \frac{y^2}{28} = 1$
$\text{ This is the required equation of the ellipse }.$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 26 Ellipse
Exercise 26.1 | Q 5.12 | Page 22