Question

Analyze the equation; that is, find the center, foci, and vertices of the given ellipse. Graph the equation.

2x^2 + 3y^2 - 8x + 6y + 5 = 0

Answer 1

Step 1:

The equation is .

Group the terms.

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 center and 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 is .

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 :