Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Find the Equation of the Hyperbola Satisfying the Given Condition : Foci (± 3 √ 5 0), the Latus-rectum = 8 - Mathematics

Find the equation of the hyperbola satisfying the given condition :

foci (± $3\sqrt{5}$ 0), the latus-rectum = 8

#### Solution

The foci of  the hyperbola  are $\left( \pm 5, 0 \right)$ and the transverse axis is 8.
Thus, the value of  $ae = 5$ and 2a = 8.

$\Rightarrow a = 4$

Now, using the relation

$b^2 = a^2 ( e^2 - 1)$, we get:

$\Rightarrow b^2 = 25 - 16$

$\Rightarrow b^2 = 9$
Thus, the equation of the hyperbola is $\frac{x^2}{16} - \frac{y^2}{9} = 1$.
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 27 Hyperbola
Exercise 27.1 | Q 11.04 | Page 14