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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
    • 5 years ago
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    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
    • 5 years ago
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    can someone help me!

  3. shadowfiend
    • 5 years ago
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    So it looks like this hyperbola is centered around (0, 0), which will make things easier.

  4. shadowfiend
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    thanks so much shadowfiend!! i really appreciate your help

  7. shadowfiend
    • 5 years ago
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    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
    • 5 years ago
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    yeah that makes sense thanks alot... how do I reward you with a medal?

  9. shadowfiend
    • 5 years ago
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    Click the `good answer' button on the right :)

  10. anonymous
    • 5 years ago
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    I'm not seeing a good answer button... sorry I'm new to this site

  11. shadowfiend
    • 5 years ago
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    Damn, really?

  12. anonymous
    • 5 years ago
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    could you point it out

  13. shadowfiend
    • 5 years ago
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    Yeah, one sec.

  14. shadowfiend
    • 5 years ago
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    Attached a screenshot showing it. Let me know if you still can't find it :)

  15. amistre64
    • 5 years ago
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    looks like shadow is hulking out :)

  16. anonymous
    • 5 years ago
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    thats so strange it doesn't show for me...

  17. shadowfiend
    • 5 years ago
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    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
    • 5 years ago
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    I WANT YOU TO GET YOUR REWARD MEDAL!!!

  19. anonymous
    • 5 years ago
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    yeah sure how do I do that?

  20. shadowfiend
    • 5 years ago
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    Are you running Windows?

  21. anonymous
    • 5 years ago
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    yes

  22. amistre64
    • 5 years ago
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    hit f5 to refresh the browser and you should see a 'good answer' beside his name

  23. shadowfiend
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    yep, mostly in internet explorer

  26. shadowfiend
    • 5 years ago
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    Ah. Well that's a doozy :p We will definitely have to take a look at why that's happening.

  27. anonymous
    • 5 years ago
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    ok I got it!

  28. amistre64
    • 5 years ago
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    f5 tends to cure it tho

  29. anonymous
    • 5 years ago
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    I just had to press f5

  30. shadowfiend
    • 5 years ago
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    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
    • 5 years ago
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    I have a similar problem if you have time

  32. shadowfiend
    • 5 years ago
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    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
    • 5 years ago
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    ok thanks!

  34. shadowfiend
    • 5 years ago
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    No problem!

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