# Math Help - Hyperbola equation help

1. ## Hyperbola 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

2. 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

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

3. Well, actually, no. If the center is at $(x_0, y_0)$, 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
$\frac{(x- x_0)^2}{a^2}- \frac{(y- y_0)^2}{b^2}= 1$