The vertices of a hyperbola are located at open paren 3 comma negative 6 close paren and open paren 3 comma 6 close paren The foci of the same hyperbola are located at open paren 3 comma negative 10 close paren and open paren 3 comma 10 close paren What is the equation of the hyperbola?

The center is the midpoint of the vertices, (3, 0), and the hyperbola opens up and down because the vertices share the same x-coordinate. The distance from the center to a vertex is a = 6, and the distance to a focus is c = 10, so b² = c² − a² = 100 − 36 = 64. Thus the equation is y²/36 − (x − 3)²/64 = 1, which is choice B.

AI-written and checked against the verified answer.