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Math Help - Hyperbola

  1. #1
    Member courteous's Avatar
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    Question Hyperbola

    Hyperbola is at the center of coordinate system. Its foci (?) are on abscissa. There are two points on the hyperbola; these are T_1(\frac{3\sqrt5}{2},2) and T_2(4,\frac{4\sqrt7}{9}). What is hyperbola's equation?
    (I'm having trouble with solving two equations that follow.)
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by courteous View Post
    Hyperbola is at the center of coordinate system. Its foci (?) are on abscissa. There are two points on the hyperbola; these are T_1(\frac{3\sqrt5}{2},2) and T_2(4,\frac{4\sqrt7}{9}). What is hyperbola's equation?
    (I'm having trouble with solving two equations that follow.)
    Since its foci are on the abscissa [x-axis] and the hyperbola is centered at the origin, we know that the hyperbola has the form \frac{x^2}{a^2}-\frac{y^2}{b^2}=1, where a>b

    Now plug the two points into this equation, and you will generate two new equations:

    At \left(4,\frac{4\sqrt{7}}{9}\right), we get \frac{16}{a^2}-\frac{112}{81b^2}=1

    At \left(\frac{3\sqrt{5}}{2},2\right), we get \frac{45}{4a^2}-\frac{4}{b^2}=1

    After solving the system of equations, I got a=\sqrt{\frac{981}{53}}

    But I'm getting b^2=-\frac{1744}{171}\implies b\text{ is complex.}

    Are you sure that you wrote down the coordinates correctly?

    --Chris
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  3. #3
    Member courteous's Avatar
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    Unhappy

    Quote Originally Posted by Chris L T521 View Post
    Are you sure that you wrote down the coordinates correctly?
    Sorry!!! No!!! Sorry, Chris! The points are T_1(\frac{3\sqrt5}{2},2) and T_2(4,\frac{4\sqrt7}{3}). The T_2 y-coordinate's denominator is 3 (not 9).
    I've done it so many times that I've automatically restarted with partially already calculated number.
    Last edited by courteous; September 19th 2008 at 03:31 AM.
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