$\"\"$

\

Observe the graph:

\

The hyperbola is vertical.

\

Standard form of the hyperbola is $\"\"$ , where $\"\"$ is center.

\

Vertices: $\"\"$ .

\

Foci: $\"\"$ .

\

Asymptotes: $\"\"$ .

\

$\"\"$ .

\

The center of the hyperbola located at $\"\"$ .

\

Therefore, $\"\"$ .

\

Length of transverse axis is $\"\"$ units.

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

Find the value of $\"\"$ .

\

The point $\"\"$ is lies on the hyperbola.

\

By the definition of the hyperbola, the absolute value of the differences from any point on the hyperbola to the foci is constant.

\

$\"\"$ .

\

Let $\"\"$ and $\"\"$ and $\"\"$ .

\

$\"\"$

\

Substitute the corresponding values in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Square on both sides.

\

$\"\"$ $\"\"$

\

$\"\"$

\

$\"\"$

\

Divide each side by $\"\"$ .

\

$\"\"$

\

Square on both sides.

\

$\"\"$ $\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Substitute the values $\"\"$ and $\"\"$ in standard form.

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

The hyperbola equation is $\"\"$ .

\