Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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# Find the Equation of the Hyperbola Satisfying the Given Condition : Vertices (0, ± 5), Foci (0, ± 8) - Mathematics

Answer in Brief

Find the equation of the hyperbola satisfying the given condition :

vertices (0, ± 5), foci (0, ± 8)

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#### Solution

The vertices of the hyperbola are $\left( 0, \pm 5 \right)$ and the foci are  $\left( 0, \pm 8 \right)$ Thus, the value of $a = 5$ and $ae = 8$

Now, using the relation

$b^2 = a^2 ( e^2 - 1)$, we get:

$\Rightarrow b^2 = 64 - 25$

$\Rightarrow b^2 = 39$

Thus, the equation of the hyperbola is  $- \frac{x^2}{39} + \frac{y^2}{25} = 1$.

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 27 Hyperbola
Exercise 27.1 | Q 11.02 | Page 14
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