The center of a hyperbola is located at the origin. one focus is located at (0, 20), and its associated directrix is represented by the line y = -256/20. what is the equation of the hyperbola?

The equation of the hyperbola is .

Step-by-step explanation:

Since directrix is , therefore the hyperbola is along the y-axis.

Focus of the hyperbola are (0,c) and (0,-c).

The given focus is (0,20), therefore the value of c is 20.

Directrix of the hyperbola is

Therefore the value of a is 16.

The relation between a, b and c is

Therefore the value of b is 12.

The standard form of the hyperbola is,

Since the value of a is 16 and the value of b is 12, therefore

D)

Step-by-step explanation:

Just took the test

a negative exponent is translated as follows:

so, we have