Question

An ellipse is represented by the equation B%5Cfrac%7B%28x%2B6%29%5E%7B2%7D%20%7D%7B144%7D" id="TexFormula1" title="\frac{(y-3)^{2} }{169 } +\frac{(x+6)^{2} }{144}" alt="\frac{(y-3)^{2} }{169 } +\frac{(x+6)^{2} }{144}" align="absmiddle" class="latex-formula">
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

Answer 1

Answer:

  C.  horizontal line that is 33.8 units

Step-by-step explanation:

We assume your equation should be ...

  $\dfrac{(y-3)^2}{169}+\dfrac{(x+6)^2}{144}=1$

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.

__

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