Find the standard formula for the hyperbola with vertices at (-7, 0) and (7, 0) and foci at (-9, 0 ) and (9, 0).

- anonymous

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- schrodinger

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- Owlfred

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

- anonymous

can someone help me!

- shadowfiend

So it looks like this hyperbola is centered around (0, 0), which will make things easier.

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## More answers

- shadowfiend

It also looks like it opens left and right.
Thus, the standard form equation should be:
\[\frac{x^2}{a^2} - \frac{y^2}{b^2}\]
That means we just have to find a and b.

- shadowfiend

To find a and b, we need to find the distance from the center to the foci. In this case, that's easy: it's 9.
That means that we have:
\[9^2 = a^2 + b^2\]
\[81 = a^2 + b^2\]

- anonymous

thanks so much shadowfiend!! i really appreciate your help

- shadowfiend

We also have the vertices of the hyperbola. We know the vertices for a hyperbola centered at (0, 0) are: (a, 0) and (-a, 0).
Since the vertices here are (7, 0) and (-7, 0), we know a = 7. Thus, we have:
\[\begin{align}
81 &= 7^2 + b^2\\
81 &= 49 + b^2\\
81 - 49 &= b^2\\
32 &= b^2
\end{align}\]
We don't need b itself, just \(b^2\), for the equation of the hyperbola. We plugin \(a^2\) and \(b^2\) and get:
\[\frac{x^2}{49} - \frac{y^2}{32} = 1\]
Does that all make sense?

- anonymous

yeah that makes sense thanks alot... how do I reward you with a medal?

- shadowfiend

Click the `good answer' button on the right :)

- anonymous

I'm not seeing a good answer button... sorry I'm new to this site

- shadowfiend

Damn, really?

- anonymous

could you point it out

- shadowfiend

Yeah, one sec.

- shadowfiend

Attached a screenshot showing it.
Let me know if you still can't find it :)

##### 1 Attachment

- amistre64

looks like shadow is hulking out :)

- anonymous

thats so strange it doesn't show for me...

- shadowfiend

That's definitely a problem. tree2193, could you post a screenshot of your screen? I definitely need to see if we can get that fixed.

- anonymous

I WANT YOU TO GET YOUR REWARD MEDAL!!!

- anonymous

yeah sure how do I do that?

- shadowfiend

Are you running Windows?

- anonymous

yes

- amistre64

hit f5 to refresh the browser and you should see a 'good answer' beside his name

- shadowfiend

Ok, cool. There should be a button somewhere with the text `prt scrn' or `print screen' or `print scrn' or some variant like that. Hit Alt+that button.

- shadowfiend

Then open Paint and hit Ctrl-V to paste it, and save that file and post it here.
amistre -- have you run into the good answer button not showing up before?

- amistre64

yep, mostly in internet explorer

- shadowfiend

Ah. Well that's a doozy :p We will definitely have to take a look at why that's happening.

- anonymous

ok I got it!

- amistre64

f5 tends to cure it tho

- anonymous

I just had to press f5

- shadowfiend

Ok, cool. Thanks to both of you. We'll see if we can figure out why IE's being silly this time.
And thanks for the medal tree2193!

- anonymous

I have a similar problem if you have time

- shadowfiend

I probably don't... But post it, and if no one else gets to it in a little while, I'll swing by and check and see what I can do.

- anonymous

ok thanks!

- shadowfiend

No problem!

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