Question

An ellipse is represented by the equation
`((y-3)^(2) )/(169 ) +((x+6)^(2) )/(144)`

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

C. horizontal line that is 33.8 units

Explanation:

We assume your equation should be ...

`((y-3)^2)/(169)+((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