Find equation of a hyperbola in standard form with center (-2,5), one vertex at (-2,8) and slope of one of its asymptotes is 3/5

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- Sep 1st 2010, 01:20 AMZoraHyperbola equation help
Find equation of a hyperbola in standard form with center (-2,5), one vertex at (-2,8) and slope of one of its asymptotes is 3/5

- Sep 1st 2010, 02:27 AMsa-ri-ga-ma
Distance between center and the vertex is a, and equation of asymptote is y = (a/b)x.

Find a and b from the given information.

So the equation of the hyperbola is

$\displaystyle \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ - Sep 1st 2010, 12:00 PMHallsofIvy
Well, actually, no. If the center is at $\displaystyle (x_0, y_0)$, the distance from the center to a vertex is a, and the equation of the asymptote is y=

**(b/a)**x, the equation of the hyperbola is

$\displaystyle \frac{(x- x_0)^2}{a^2}- \frac{(y- y_0)^2}{b^2}= 1$