Question

Use a graphing utility to graph the ellipse. Find  the  center,  foci,  and  vertices.  (Recall  that  it  may  be necessary to solve the equation for y and obtain two equations.)

12x^2 + 20y^2 - 12x + 40y - 37 = 0

Answer 1

Step 1:

The ellipse equation is .

Write the equation in standard form of ellipse.

Complete the each square.

Compare it to standard form of the ellipse equation is .

Here , so major axis is parallel to axis.

Where,

is the center of the ellipse.

is the length of the semi major axis.

is the length of the semi minor axis.

is the distance between the center and the focus.

.

Step 2 :

The center of the ellipse is .

The vertices of the ellipse are .

The foci of the ellipse are .

The end points of the minor axis are .

Graph :

(1) Draw the coordinate plane.

(2) Plot the center, foci and vertices.

(3) Draw the equation of the ellipse.

Solution :

The center of the ellipse is .

The vertices of the ellipse are .

The foci of the ellipse are .

Graph of the ellipse :