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Math Help - Finding equation of hyperbola from known coordinates of focii

  1. #1
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    Finding equation of hyperbola from known coordinates of focii

    I've been having problems with one particular one. here it is
    "Find the equation of the hyperbola if its focuses are F_1=(10,-2)F_2=(16,2) and 2a=24.

    Any help is greatly appreciated

    Regards,
    Rinor
    Last edited by mr fantastic; January 27th 2009 at 11:30 AM.
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  2. #2
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    Quote Originally Posted by Rinor Berisha View Post
    I've been having problems with one particular one. here it is
    "Find the equation of the hyperbola if its focuses are F_1=(10,-2)F_2=(16,2) and 2a=24.

    Any help is greatly appreciated

    Regards,
    Rinor
    The only way I found is: Use the definition of the hyperbola.

    Let P denote any arbitrary point on the hyperbola. Then the equation must be true:

    |\overline{PF_1}| - |\overline{PF_2}| = 2a

    But I hope for you that the original question reads:

    "Find the equation of the hyperbola if its focuses are F_1={\bold{(-10,2)}},~F_2=(16,2) and 2a=24.

    If so:
    1. The center is at C(3, 2)
    2. e = 13
    3. From e=\sqrt{a^2+b^2} follows b = 5
    4. The equation of the hyperbola is: ....... \dfrac{(x-3)^2}{144}-\dfrac{(y-2)^2}{25}=1
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