Can someone help walk me through this problem? I'd really appreciate your help.
Find an equation in standard form for the hyperbola with vertices at (0, -10) and asymptotes at y= +-(5/4)x
If the transverse axis is on the y-axis, then the form of the hyperbola is:
$\displaystyle \frac{y^2}{a^2}-\frac{x^2}{b^2}=1$ where $\displaystyle 0<a,b$.
Since the vertices are (presumably) at $\displaystyle (0,\pm10)$, then what is the value of a?
The asymptotes will be at $\displaystyle y=\pm\frac{a}{b}x$, so from the given asymptotes, we know:
$\displaystyle \frac{a}{b}=\frac{5}{4}$
$\displaystyle b=\frac{4}{5}a$
Use the value you found for a to find b.
and so what is the equation of the hyperbola?