SOLUTION: Find the vertex, focus, and directrix of the parabola given by x^2-10x-8y+33=0 I think: x^2-10x=8y-33 but I'm not sure what to do from there. Please explain the steps to m

Question 145166: Find the vertex, focus, and directrix of the parabola given by
x^2-10x-8y+33=0
I think:
x^2-10x=8y-33
but I'm not sure what to do from there.
Please explain the steps to me if you can, thanks for your help!

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
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:

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

, so and the focus is at (,), the vertex is at (,), and the directrix is
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