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

x = -27/5

X^2 - 4x +(4/2^2) + y^2 + 8y + (8/2^2) = -4 + (4/2^2) + (8/2^2)(x + 2)^2 + (y + 4)^2 = -4 + 4 + 16your center is (-2, -4) and the radius is the sqrt of -4 + 4 + 16 which is 4