The center of an ellipse is located at open paren 0 comma 0 close paren One focus is located at open paren 12 comma 0 close paren , and one directrix is at x is equal to 14 and 1 over 12 Which equation represents the ellipse?

The focus at (12, 0) means the ellipse’s focal distance is c = 12, and its major axis is horizontal. For a horizontal ellipse, the directrix is at x = a²/c. Since the directrix is x = 14 1/12 = 169/12, we get a²/12 = 169/12, so a² = 169. Then b² = a² − c² = 169 − 144 = 25. The equation is x²/169 + y²/25 = 1, which is choice A.

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