# If the Distance Between the Foci of a Hyperbola is 16 and Its Ecentricity is √ 2 ,Then Obtain Its Equation. - Mathematics

If the distance between the foci of a hyperbola is 16 and its ecentricity is $\sqrt{2}$,then obtain its equation.

#### Solution

We have

$2ae = 16$

$\Rightarrow ae = 8$

$\Rightarrow a = \frac{8}{\sqrt{2}} = 4\sqrt{2}$

$\Rightarrow a^2 = 32$

Now,

$\left( ae \right)^2 = a^2 + b^2$

$\Rightarrow \left( 8 \right)^2 = 32 + b^2$

$\Rightarrow 64 - 32 = b^2$

$\Rightarrow b^2 = 32$

Therefore, the equation of the hyperbola is given by

$\frac{x^2}{32} - \frac{y^2}{32} = 1$

$\Rightarrow x^2 - y^2 = 32$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 27 Hyperbola
Exercise 27.1 | Q 12 | Page 14