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14 December, 02:08

The foci and the directrices of the hyperbola are labeled. Which equation represents the hyperbola? (x-3) ^2/16 - y^2/9 = 1 x^2/16 - (y-3) ^2/9 = 1 (y-3) ^2/9 - x^2/16 = 1 y^2/9 - (x-3) ^2 = 1

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  1. 14 December, 02:21
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    Step-by-step explanation:

    Hyperbola are generally written as

    (x-h) ² / a² - (y-k) ² / b² = 1

    Where,

    (h, k) is the center is

    "a" is the semi-transverse axis

    "b" is the semi-conjugate axis

    The focus and the directives is generally describe as

    The foci of the graph are

    (h + a⋅e, k) and (h - a⋅e, k)

    The directrices of the graph are

    x = h + a / e and x = h - a / e

    Comparing this to the equation given

    1. (x-3) ² / 4² - y² / 3² = 1

    This is an hyperbole of centre (3,0)

    And parallel to the x axis

    2. x² / 4² - (y-3) ² / 3² = 1

    This is also an hyperbole of center (0,3) and parallel to the x axis

    3. (y-3) ² / 3² - x² / 4² = 1

    This is an hyperbole parallel to the x axis

    4. y² / 3² - (x-3) ² / 1² = 1

    This is an hyperbole parallel to the y-axis
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