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Math Help - Ellipses standard form

  1. #1
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    Ellipses standard form

    Find the standard form of the equation of the hyperbola with the given characteristics.

    Vertices: (-2,1),(2,1);
    passes through the point (5,4)
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  2. #2
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    The equation of a hyperbola is given by \frac{(x-h)^2}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1, where (h,k) is the centre of the hyperbola.

    For your question, the centre of the hyperbola is (0,1), and a=2 since a is the distance from the vertices to the centre.

    Thus, \frac{(x-0)^2}{2^{2}}-\frac{(y-1)^{2}}{b^{2}}=1

    Since the curve passes through (5,4), you can find b^{2} by substitution.
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