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

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

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- May 9th 2012, 06:21 AMaab300Hyperbola Problem
(x^2)/25 - (y^2)/(b^2)=1

Find the directrices, foci, and eccentricity of hyperobola???? - May 9th 2012, 11:37 AMearbothRe: Hyperbola Problem
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:

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

Thus the foci have the coordinates:

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

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

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

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