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22 August, 05:18

An ellipse has a vertex at (14, - 1). The focus of the ellipse nearest that vertex is located at (8, - 1). If the center of the ellipse is located at (-1, - 1), what is the equation of the directrix on that side of the ellipse?

x =

+5
Answers (2)
  1. 22 August, 07:09
    0
    The answer is 24, I just did the assignment ...

    you're welcome!
  2. 22 August, 09:13
    0
    Refer to the diagram shown below.

    The right vertex is at (14, - 1), and the center is at (-1, - 1).

    Therefore the semi-major axis is

    a = 14 - (-1) = 15

    The right focus is at (8, - 1).

    Therefore

    c = 8 - (-1) = 9.

    The distance of the directrix from the center is

    d = c²/a = 9²/15 = 81/15 = 27/5.

    Therefore the equation for the left directrix is

    x = - 1 - 27/5 = - 32/5

    Answer: x = - 27/5
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