Originally Posted by
TomJerry For finding the shape of the hyperbola, trace the equation $\displaystyle \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$
$\displaystyle \frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1 $
whereby
$\displaystyle c^2 = a^2 + b^2 $ .
In your hyperbola, (h,k) = (0,0), so we have a start to this: The center is at the origin.
Note that if
$\displaystyle \frac{(y-k)^2}{b^2} - \frac{(x-h)^2}{a^2} = 1 $
then the transverse axis would be vertical. However, the way we have it, with the x-term positive and the y-term negative, the traverse axis is horizontal