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ERoseM

  • 2 years ago

The equation of a hyperbola is given by: 25x^2-16y^2+100x+96y=144 Rewrite the equation in standard form

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  1. dpaInc
    • 2 years ago
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    ok.. it's complete the square time.. |dw:1337817367153:dw|

  2. dpaInc
    • 2 years ago
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    do you what you need in that first parenthesis to make it into a perfect square trinomial?

  3. ERoseM
    • 2 years ago
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    Yes, I do. It would be 4 in the first parenthesis and 9 in the second, correct? I am confused on what to do after that because the number on the other side of the equal sign is actually 444

  4. dpaInc
    • 2 years ago
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    yes... you're correct

  5. dpaInc
    • 2 years ago
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    whatever you do to one side, you do to the other.... |dw:1337817614794:dw|

  6. ERoseM
    • 2 years ago
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    Yes, and then I get 400 on the right side and I'm unsure how to apply that to the other side.

  7. dpaInc
    • 2 years ago
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    |dw:1337817875892:dw|

  8. ERoseM
    • 2 years ago
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    |dw:1337817783416:dw|

  9. dpaInc
    • 2 years ago
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    |dw:1337817942410:dw|

  10. dpaInc
    • 2 years ago
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    oh... you're way ahead of me... :)

  11. ERoseM
    • 2 years ago
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    Is that right though? Is there anyway I can check the process because sometimes I keep going and it turns out wrong?

  12. dpaInc
    • 2 years ago
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    shouldn't the right side be 100?

  13. dpaInc
    • 2 years ago
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    |dw:1337818132008:dw|

  14. ERoseM
    • 2 years ago
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    144 is actually 444. I typed it in wrong originally and then explained it after

  15. dpaInc
    • 2 years ago
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    ooh ok, so the right side is 400..

  16. dpaInc
    • 2 years ago
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    the process is correct... if there are no calculation errors, the equation is correct.

  17. dpaInc
    • 2 years ago
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    the equation you ended up with...

  18. ERoseM
    • 2 years ago
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    |dw:1337818278093:dw|

  19. dpaInc
    • 2 years ago
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    yes.. do you know where the center is?

  20. ERoseM
    • 2 years ago
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    It would be (-2, -3) right? And its horizontal? How can I tell..I'm confused on when its different? Is a just always bigger?

  21. dpaInc
    • 2 years ago
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    wait...

  22. dpaInc
    • 2 years ago
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    this should be negative.... right? |dw:1337818435775:dw|

  23. ERoseM
    • 2 years ago
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    Yes. Darn it. I should have seen that. Thank you

  24. dpaInc
    • 2 years ago
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    here's your verification : center is at (-2, 3) http://www.wolframalpha.com/input/?i=center+25x%5E2-16y%5E2%2B100x%2B96y%3D144

  25. ERoseM
    • 2 years ago
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    Thank you! That's perfect! The equation is horizontal right?

  26. dpaInc
    • 2 years ago
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    equation?

  27. dpaInc
    • 2 years ago
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    oh... yes.. this is a horizontal or left/right branch hyperbola...

  28. dpaInc
    • 2 years ago
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    good work...

  29. ERoseM
    • 2 years ago
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    And so a would be 4? Because in standard form it is 16 which is a^2?

  30. dpaInc
    • 2 years ago
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    yes... a=4 b= c=

  31. ERoseM
    • 2 years ago
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    b=5 and c= the square root of 41?

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