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8 January, 21:08

Write the equation of a hyperbola with vertices (3, - 1) and (3, - 9) and co-vertices (-6. - 5) and (12, - 5).

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  1. 8 January, 21:23
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    The answer:

    the main formula of hyperbola is

    (x-h) ² / a² - (y-k) ² / b² = 1, where the center is C (h, k)

    and the vertex formmula is

    (h+-a, k) and the covertex is (h, k+-b)

    in our case vertices are already given:

    (3, - 1) and (3, - 9) so h+a = 3 or h - a = 3 and k = - 1, or k = - 9

    and co-vertices (-6. - 5) and (12, - 5)

    h = - 6 or h = 12, and k + b=-5, or k - b = - 5

    for example h = - 6, h+a = 3, a=3+6=9, k = - 1, k + b=-5, we can get b = - 5 + 1 = - 4, so a=9, b=-4, h=-6, k = - 1

    the equation is

    (x+6) ² / 81 - (y+1) ² / 16 = 1, if the center is C (-6, - 1)

    the same method can be applied with the other choices of h and k.
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