Given that $x^2-bx+17-ay=0$ has vertex $(3,2)$, find the directrix and focus.
My attempt is to make it into the form $(x-h)^2=4a(y-k)$ which has focus $(h,k+a)$ and directrix $y=k-a$. Is this right?
$x^2-bx+17-ay=0$
$(x-\frac{b}{2})^2=4(\frac{a}{4})(y-(-\frac{b^2}{4a}+\frac{17}{a}))$ has vertex $(3,2)$ iff
$\frac{b}{2}=3$
$-\frac{b^2}{4a}+\frac{17}{a}=2$
Solving this gets me a=4 and b=6 so the focus is $(h,k+a)$=$(3,2+4)$=$(3,6)$,
and the directrix is $y=k-a=2-4=-2$