Question

Find an equation for the given ellipse. Graph the equation.

Center at (2, - 2);       Vertex at (7, - 2);          focus at  (4, - 2)

Answer 1

Step 1 :

The center of the ellipse is .

The focus of the ellipse is .

The vertex of the ellipse is .

The  - coordinate of vertices and focus are same, so the ellipse is horizontal.

The standard form of ellipse is ,

where is the center of the ellipse, is the length of the major axis and is the length of the minor axis.

The distance between center and vertex is .

The distance between center and focus is .

.

Step 2 :

The length of major axis is the distance between center and vertex.

is the distance between center and focus.

Now .

Substitute the values of , and in standard form of ellipse.

The equation of ellipse is .

Step 3 :

Graph the ellipse.

Graph the equation .

Plot the center point .

Plot the focus points and .

Plot the vertex points and .

Plot the two points above and below the center and .

Solution :

The equation of ellipse is .

The graph of the ellipse is :