An ellipse is represented by the equation
Each directrix of this ellipse is a from the center on the major axis.

A. horizontal line that is 5 units
B. vertical line that is 5 units
C. horizontal line that is 33.8 units
D. vertical line that is 33.8 units

  C.  horizontal line that is 33.8 units

Step-by-step explanation:

We assume your equation should be ...

The largest denominator in this standard-form equation of an ellipse is under the y-term, so the major axis is vertical. The directrix will be a horizontal line.

The distance from the center to the directrix is always longer than the semi-major axis, so will be more than √169 = 13. This only leaves choice C.

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If "c" is the center-to-focus distance, it will be the root of the difference of the denominators in the equation:

  c = √(169 -144) = 5

For semi-major axis "a", the distance from the center to the directrix is ...

  a²/c = (13²)/5 = 33.8 . . . . . matches choice C

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