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

Given:

Hyperbola with directrices at y = ±2 and foci at (0, 6) and (0, −6).

To find:

The equation of hyperbola.

Solution:

We have, directrices at y = ±2 so this hyparabola is along the y-axis.

The standard form of hyperbola is

     ...(i)

where, (h,k) is center, foci are and directrix are .

On comparing foci, we get

On comparing directrix we get

Now,

Putting , we get

Therefore, the equation of hyperbola is .

answer: 800

step-by-step explanation: