Question

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

4x^2 - y^2 = 16

Answer 1

Step 1:

The equation is .

Divide each side by 16.

Compare the above equation with .

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

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 and .

(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 .