$\"\"$

The vertex of the hyperbola is $\"\"$ .

The $\"\"$ -coordinate of the vertices are equal, hence the hyperbola is vertical.

$\"\"$ .

Therefore, $\"\"$ and $\"\"$ .

Point on the graph is $\"\"$ .

The equation of the vertical hyperbola is $\"\"$ .

$\"\"$

Point $\"\"$ lies on the hyperbola.

$\"\"$

The equation of the hyperbola is $\"\"$ .

$\"\"$

$\"\"$ .

$\"\"$

The equation of the hyperbola is $\"\"$ .