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I am totally stuck if someone can help me find the center I can figure out the rest

is the center 0,0

http://tutorial.math.lamar.edu/Classes/Alg/Hyperbolas.aspx
is a good link to help you!

I am just really confused because there is nothing on the bottom for a denominator

I'm not sure myself, but it looks like it's (1,2) for the center.

so the center is (1,3)

\[\frac{9}{1}=\frac{1}{\frac{1}{9}}=\frac{1}{(\frac{1}{3})^2}\]

so this would make it the last picture right

this one

If the center is (1,2) that is your only option!

Did you check out the link?
http://tutorial.math.lamar.edu/Classes/Alg/Hyperbolas.aspx

yes

centre would be (1,2) i think so

Well that's two of us. I say it's a good bet.

sometimes the pictures are just hard to go by

but we know that it is not (0,0) or (-1,2) so the last one is the best

thank you

When you look at \[(x-h)^2\], \[(x-h)\]is how you are modifying x. You are finding the difference between them with subtraction.
Then that difference is squared, so only the difference between them matters, not at all whether x>h or x