parabola focal width

Question

What is the focal width of the parabolic equation $y=x^2-8x-18$?

I have pretty much all of the other vital numbers (vertex is $(4,-34)$, focus $(4, -\frac{87} 4$)) but am having a problem figuring the focal width.

I concur with the focal distance result already given by KittyL. It should be commented that the $ \ y-$ coordinate you give for the focus must then be incorrect. (It is "above" the vertex, but not that far up...) — colormegone, Jun 12 '15 at 23:08

score 1 · Answer 1 · answered Jun 12 '15 at 17:31

1

The focal width of the parabola $(x-h)^2=4p(y-k)$ is $|4p|$.

If you know the vertex, you must know how to transform it to this standard form $$(x-4)^2=y+34$$

So the focal width is $|4p|=1$.

answered Jun 12 '15 at 17:31

KittyL

1 Answers1