The vertices of hyperbola are and its foci are .

Since the vertices and foci points have the same y - coordinate, the transverse axis parallel to the x - axis.

So, the hyperbola has a horizontal 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 center of the hyperbola at the midpoint of its vertices.

Thus, the center is .

The foci of hyperbola are .

From foci point the x - coordinate :

.

.

The vertices of hyperbola are .

From vertices point the x - coordinate : \ \ .

.

Consider .

. \ \

Substitute the values of and in .

.

Thus, the equation of the hyperbola is .

The equation of the hyperbola is .