A hyperbola has its foci at open paren 7 comma 5 close paren and open paren 7 comma negative 5 close paren A directrix of the hyperbola is y is equal to 16 fifths What is the equation of the hyperbola?

The foci have midpoint (7, 0), so the center is (7, 0), and the hyperbola opens vertically because the foci differ in their y-coordinates. For a vertical hyperbola, the directrix is y = k + a²/c; here 16/5 = a²/5, so a² = 16. Since c² = a² + b² and c = 5, b² = 25 − 16 = 9. Thus the equation is y²/16 − (x − 7)²/9 = 1, which is choice A.

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