Ellipse Construction Applet
The point (h,k) is the center. a is the major radius and b is the minor radius.
If the ellipse is horizontal, use points E and F for the foci and lines f and g to help with the construction. Activate i and j to see the segments from the foci to the point on the ellipse. Activate point D, the point on the ellipse. Now drag point B around the circle and watch the construction.
If the ellipse is vertical, use points H and I for the foci and lines m and n to help with the construction. Activate p and q to see the segments from the foci to the point on the ellipse. Activate point G. Now drag point B around the cirlce to watch the construction.