Question

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

Center at (1, 2);     Vertex at (4, 2);      Contains the point  (1, 5)

Answer 1

Step 1 :

The center of the ellipse is .

The vertex of the ellipse is .

The point on the ellipse is .

The  - coordinate of vertex and center 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.

The ellipse contains the point .

Let the point is .

Substitute the point , and the center in standard form of ellipse.

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

The equation of ellipse is .

Step 3 :

Graph the equation .

Plot the center point .

Plot the vertex points and .

Plot the two points above and below the center and .

Since the major axis length is equal to the minor axis length, the curve represents a circle.

Solution :

The equation of ellipse is .

The graph of the equation is :

Since the major axis length is equal to the minor axis length, the curve represents a circle.