Question

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

 Foci at (0, ±3);      x - intercepts are ±2

Answer 1

Step 1:

Foci of the ellipse and -intercepts are

In this case -intercepts are co-vertices of the ellipse.

Co-vertices are end points of minor axis.

Mid point of co-vertices is center of the ellipse.

The -coordinate of foci is 0. So the required ellipse is vertical.

The standard form of vertical ellipse is .

Where

  is length of semi major axis and is length of semi minor axis.

Center is , vertices

Co-vertices

Foci .

Where .

Step 2:

Foci =

Substitute in above equation.

Co-vertices = .

Substitute in above equation.

Vertices of the ellipse are .

Comments

Contd..

Step 3:

Substitute , and in standard form.

The equation is .

Graph:

Draw the coordinate plane.

Plot the center, vertices, co-vertices and foci of the ellipse.

Sketch the ellipse by using semi major axis length and semi minor axis length.

.

Solution:

The ellipse equation is and the graph of ellipse is:

.