Question

Find an equation of the hyperbola.

Center: (0, 0)

Vertex: (0, 2)

Focus: (0, 4)

Answer 1

Step 1:

The hyperbola center is , focus is and vertex is .

Observe the points, here coordinates are equal.

So, the hyperbola has a vertical transverse axis and its standard form of the equation is

.

Where, is the center.

is the distance between center and vertex.

is the distance between center and focus.

.

The distance between center and vertex is .

The distance between center and focus is .

Substitute the values of ,  and  in standard form of the equation.

The equation of hyperbola is .

Solution:

The equation of hyperbola is .