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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