Step 1:

The equation is .

Group the terms.

Add 1 to each side.

Complete each square.

Compare the above equation with .

So the equation is in the standard form of the hyperbola.

The center of the hyperbola is .

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Step 2:

The hyperbola has a transverse axis parallel to axis.

The foci of the hyperbola is .

The vertices of the hyperbola is .

Find the points to form a rectangle.

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

Asymptotes of the hyperbola are .

Substitute the values of in .

Asymptotes are .

Step 3:

Graph :

(1) Draw the coordinate plane.

(2) Draw the equation of the hyperbola.

(3) Plot the foci and vertices.

(4) Form a rectangle containing the points , .

(5) Draw the asymptotes of the hyperbola.

Solution :

The center of the hyperbola is .

The hyperbola has a transverse axis parallel to axis.

The vertices of the hyperbola is .

The foci of the hyperbola is .

Asymptotes of the hyperbola are .