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## anonymous 5 years ago Find the standard formula for the hyperbola with vertices at (-7, 0) and (7, 0) and foci at (-9, 0 ) and (9, 0).

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1. 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!

2. anonymous

can someone help me!

3. shadowfiend

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

4. 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.

5. 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: $9^2 = a^2 + b^2$ $81 = a^2 + b^2$

6. anonymous

thanks so much shadowfiend!! i really appreciate your help

7. 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?

8. anonymous

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

9. shadowfiend

Click the good answer' button on the right :)

10. anonymous

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

11. shadowfiend

Damn, really?

12. anonymous

could you point it out

13. shadowfiend

Yeah, one sec.

14. shadowfiend

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

15. amistre64

looks like shadow is hulking out :)

16. anonymous

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

17. 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.

18. anonymous

I WANT YOU TO GET YOUR REWARD MEDAL!!!

19. anonymous

yeah sure how do I do that?

20. shadowfiend

Are you running Windows?

21. anonymous

yes

22. amistre64

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

23. 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.

24. 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?

25. amistre64

yep, mostly in internet explorer

26. shadowfiend

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

27. anonymous

ok I got it!

28. amistre64

f5 tends to cure it tho

29. anonymous

I just had to press f5

30. 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!

31. anonymous

I have a similar problem if you have time

32. 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.

33. anonymous

ok thanks!

34. shadowfiend

No problem!

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