$\"\"$

\

The hyperbola foci is at $\"\"$ and $\"\"$ and asymptote line is $\"\"$

\

The $\"\"$ - coordinates of the foci are equal.

\

The standard form of the hyperbola has a horizontal transverse axis is $\"\"$ .

\

Where $\"\"$ is the center.

\

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

\

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

\

The distance between center and foci 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 $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$ \ \

\

$\"\"$ . \ \

\

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

\

$\"\"$ . \ \

\

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

\

$\"\"$ . \ \

\

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

\

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

\

Substitute $\"\"$ . \ \

\

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

\

The vertices of hyperbola is $\"\"$ . \ \

\

Substitute $\"\"$ . \ \

\

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

\

Find the points above and below the center by susbtituting $\"\"$ in $\"\"$ . \ \

\

$\"\"$ \ \

\

$\"\"$ \ \

\

$\"\"$ . \ \

\

The points above and below center 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: \ \

\

$\"\"$ .