Question

Find an equation for the hyperbola described.Graph the equation.

Center at (0, 0);  focus at (0, - 6);  vertex at (0, 4)

Answer 1

Step 1:

The hyperbola center is at , focus is at and vertex is at .

Observe the points, here coordinates are equal.

So, the hyperbola has a vertical transverse axis and its standard form of the equation is

.

Where,

is the center.

is the distance between center and vertex.

is the distance between center and focus.

.

The distance between center and vertex is .

The distance between center and focus is .

Substitute the values of in standard form of the equation.

Step 2:

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 center, foci and vertices.

(4) Form a rectangle containing the points and .

(5) Draw the asymptotes of the hyperbola.

Solution :

The equation of the hyperbola is .

Graph of the hyperbola :