$\"\"$

\

The hyperbola vertices at $\"\"$ and $\"\"$ and asymptote line at $\"\"$

\

The $\"\"$ - coordinates of the focus and vertex are equal.

\

The standard form of the hyperbola has a vertical transverse axis is

\

$\"\"$ .

\

Where, $\"\"$ is the center.

\

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

\

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

\

The center is the mid point point of vertices of the hyperbola.

\

Center $\"\"$ .

\

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

\

The extensions of the diagonals of the rectangle are the asymptotes of the hyperbola

\

Asymptotes of the hyperbola are $\"\"$ .

\

Compare the asymptote $\"\"$ with general form.

\

$\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$ .

\

Substitute $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$

\

Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$ .

\

Therefore, the equation of the hyperbola is $\"\"$ .

\

$\"\"$

\

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

\

Substitute $\"\"$ and $\"\"$ .

\

$\"\"$

\

The foci is at $\"\"$ and $\"\"$ .

\

Find the points to form a rectangle.

\

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

\

Asymptotes are $\"\"$ and $\"\"$ . $\"\"$

\

Graph :

\

(1) Draw the coordinate plane.

\

(2) Draw the equation of the hyperbola.

\

(3) Plot the center, foci and vertices.

\

(4) Form a rectangle containing the points $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

\

(5) Draw the asymptotes of the hyperbola.

\

$\"\"$

\

$\"\"$

\

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

\

Graph of the hyperbola :

\

$\"\"$ .