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14 May, 11:12

Which of the following is the equation of a hyperbola with center at (0, 0), with a = 4, b = 1, opening horizontally?

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  1. 14 May, 12:39
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    The equation of the hyperbola is x²/16 - y²/1 = 1

    Step-by-step explanation:

    * Lets study the equation of the hyperbola

    - The standard form of the equation of a hyperbola with

    center (0, 0) and transverse axis parallel to the x-axis is

    x²/a² - y²/b² = 1

    # The length of the transverse axis is 2a

    # The coordinates of the vertices are (±a, 0)

    # The length of the conjugate axis is 2b

    # The coordinates of the co-vertices are (0, ±b)

    # The coordinates of the foci are (± c, 0),

    # The distance between the foci is 2c where c² = a² + b²

    * Now lets solve the problem

    ∵ The center of the hyperbola is (0, 0)

    ∵ It is opening horizontally

    ∴ x²/a² - y²/b² = 1

    ∵ a = 4, b = 1

    ∴ a² = (4) ² = 16

    ∴ b² = (1) ² = 1

    ∴ x²/16 - y²/1 = 1

    ∴ The equation of the hyperbola is x²/16 - y²/1 = 1
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