i have given equations:

$\displaystyle x^2-y=3$ <== parabola I already got this one.

$\displaystyle 4x^2-y^2+2y=5$ ==> how to form into general form $\displaystyle \frac {(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}$?

This i have this far:

$\displaystyle 4x^2-(y^2+2y+1)=5+4-1$

$\displaystyle 4(x-0)^2 - (y+2)^2 = 8$

$\displaystyle \frac {(x-0)^2}{2}-\frac{(y+2)^2}{8}=1$

$\displaystyle a=\sqrt(2), b=\sqrt(8), and (h,k) = (0,-2)$

Am I wrong or right? thanks in advance////