Question 145166
Good start.  You have correctly completed the first step.


Next step:  Complete the square on the x terms.  Divide the coefficient on the 1st degree x term by 2 and square it.  Add the result to both sides of the equation.  That will give you a perfect square on the left, thus:


{{{x^2-10x+25=8y-33+25}}}
{{{(x-5)^2=8(y-1)}}}


Now your equation is in the form {{{(x-h)^2=4p(y-k)}}} which is a parabola with:
Vertex at (h,k),
Focus at (h,k+p), and
Directrix y = k - p


{{{4p=8}}}, so {{{p=2}}} and the focus is at ({{{5}}},{{{3}}}), the vertex is at ({{{5}}},{{{1}}}), and the directrix is {{{y=-1}}}