Which is the equation of a hyperbola with directrices at y = ±2 and foci at (0, 6) and (0, −6)?

A) x squared over 12 minus y squared over 24 equals 1
B) x squared over 12 minus y squared over 48 equals 1
C) y squared over 12 minus x squared over 24 equals 1
D) y squared over 48 minus x squared over 12 equals 1

Step-by-step explanation:

The directrices are at and .

The focuses are and.

Notice that each focus is on the y-axis, which means this is a vertical hyperbola. Also, we know that .

So, the hyperbola should have the form

Therefore, the equation of this hyperbola is

Because, it matches the given information, this equation giives a parabola with the right focuses, and directrices.

So, the right answer is C.

step-by-step explanation: