One focus of a hyperbola is located at (−1, 7). One vertex of the hyperbola is located at (−1, 5). The center is (−1,−3). What is the equation of the hyperbola?

The focus and vertex have the same x-coordinate as the center, so the hyperbola opens up and down. The vertex is 8 units from the center, so a² = 8² = 64; the focus is 10 units from the center, so c² = 10² = 100. For a hyperbola, c² = a² + b², giving b² = 100 − 64 = 36. Centered at (−1, −3), its equation is (y + 3)²/64 − (x + 1)²/36 = 1, which is choice C.

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