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 $\"\"$ .