Step 1:

The vertices are $\"\"$ and foci are $\"\"$ .

Observe vertices and foci, $\"\"$ 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.

$\"\"$ .

By the midpoint formula, the center of the hyperbola is $\"\"$ .

The distance between center and vertex is $\"\"$ .

The distance between center and focus is $\"\"$ .

$\"\"$

Substitute the values of $\"\"$ in standard form of the equation.

$\"\"$

Solution :

The standard form of the hyperbola $\"\"$ .