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Math Help - need help on hyperbola

  1. #1
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    need help on hyperbola

    find the equation of the hyperbola:
    center at (0,0) transverse axis along the x-axis, passing through the points (3,5), (2,-3).
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  2. #2
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    find the equation of the hyperbola:
    center at (0,0) transverse axis along the x-axis, passing through the points (3,5), (2,-3).
    Hi,

    the general equation of such a hyperbola is:

    x/a - y/b = 1 with a and b as the semi-axes.

    You know the coordinates of 2 points which must satisfy this equation:

    i) 9/a - 25/b = 1

    ii) 4/a - 9/b = 1

    From i) you get

    iii) a = (9b)/(b + 25).

    Plug this term for a into the equation at ii):

    4/((9b)/(b + 25)) - 9/b = 1. Solve for b.

    I've got b = 19/5. Substitute this value into the equation at iii). You'll get

    a = 19/16.

    The equation of the hyperbola becomes:

    x/(19/16) - y/(19/5) = 1 <===> (16x)/19 - (5y)/19 = 1

    EB
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