Question

The center of an ellipse is located at (0, 0). One focus is located at (12, 0), and one directrix is at x = 14 1/12.

Answer 1

The standard equation for an ellipse is
$\frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} =1$
where
(h,k) = coordinates of the center
a, b = semi-major and semi-minor axes

Refer to the figure shown below.
The center of the ellipse is at (0,0). 
Therefore, h=0, k=0.

One focus is at (12, 0)
Therefore
c = 12

One directrix is at  14 1/12 = 169/12.
Because the directrix is located at x = a²/c, therefore
a²/12 = 169/12
a² = 169/144
a = 13

Because c² = a² - b², obtain
b² = a² - c²
     = 169 - 144 = 25
b = 5

Answer:
The equation for the ellipse is
$\frac{x^{2}}{169} + \frac{y^{2}}{25} =1$

Answer 2

Answer:

Its A

Step-by-step explanation:

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