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 =

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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