Question

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

Foci at (±2, 0);    length of the major axis is 6

Answer 1

Step 1 :

The foci of the ellipse : .

Length of the major axis is .

Since the - coordinate of foci are same, the ellipse is horizontal.

The standard form of the ellipse is .

Where, center as an origin, ,

Foci , .

Vertices .

  is the length of the major axis and

is the length of the minor axis.

Step 2 :

The foci of the ellipse : = .

.

Length of the major axis : .

.

Now .

Substitute the values of and in .

The equation of ellipse is 

Step 3 :

Graph the ellipse.

Graph the equation

Plot the center point .

Plot the focus points .

Plot the vertex points .

Plot the two points above and below the center and .

Solution :

The equation of ellipse is

The graph of the ellipse :