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