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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)

 

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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
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