Question

Find the center,transverse axis,vertices,foci,and asymptotes.Graph the equation.

x^2 - y^2 - 2x - 2y - 1 = 0

Answer 1

Step 1:

The equation is .

Group the like terms.

Add 1 to each side.

Complete each square.

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

Compare the above equation with .

The center of the hyperbola is .

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.

.

.

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 .

Graph of the hyperbola :