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  • If the distance between the foci of a hyperbola is 16 and its eccentricity is square root of 2, then obtain the equation of the hyperbola

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

Answers (1)

Let the equation of the hyperbola be \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1

Distance between foci=2ae=16

e=\sqrt{2}

a=4\sqrt{2}
We know that b=\sqrt{a^{2}\left ( 1-e^{2} \right )}=\sqrt{32}

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

x2-y2=32

Posted by

infoexpert22

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