The vertices of a hyperbola are located at open paren negative 4 comma 1 close paren and open paren 4 comma 1 close paren The foci of the same hyperbola are located at open paren negative 5 comma 1 close paren and open paren 5 comma 1 close paren What is the equation of the hyperbola?

The vertices are at (−4, 1) and (4, 1), so the center is (0, 1) and the hyperbola opens horizontally. The distance from the center to a vertex is a = 4, and the distance to a focus is c = 5. Using c² = a² + b² gives b² = 25 − 16 = 9, so the equation is x²/16 − (y − 1)²/9 = 1, choice A.

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