Hyperbola Problem

**aab300** · May 9th 2012, 06:21 AM

(x^2)/25 - (y^2)/(b^2)=1

Find the directrices, foci, and eccentricity of hyperobola????

**earboth** · May 9th 2012, 11:37 AM

Originally Posted by aab300

(x^2)/25 - (y^2)/(b^2)=1

Find the directrices, foci, and eccentricity of hyperobola????

It would be much easier for us to help you if you have shown some work, because this question is quite straight forward.

Your equation describes a family of hyperbolae with the properties:

$e^2 = a^2+b^2~\implies~e^2=25+b^2$

Thus the foci have the coordinates:

$F_1\left(-\sqrt{25+b^2}, 0 \right) ; F_2\left(\sqrt{25+b^2}, 0 \right)$

The numerical eccenticity is $\epsilon = \frac ea$

and therefore the equation of the directrice is $D: x = \epsilon$

Since $b > 0 ~\implies~\epsilon > 1$

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