One focus of a hyperbola is located at open paren negative 6 comma 2 close paren One vertex of the hyperbola is located at open paren negative 4 comma 2 close paren The center is open paren negative 1 comma 2 close paren What is the equation of the hyperbola?

The focus, vertex, and center all have the same y-coordinate, so the hyperbola opens horizontally. The vertex is 3 units from the center, giving a² = 9, and the focus is 5 units from the center, giving c² = 25. Since c² = a² + b², b² = 25 − 9 = 16. With center (−1, 2), the equation is (x + 1)²/9 − (y − 2)²/16 = 1, which is choice C.

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