Arcs of Circle Method
The arc of circle method of drawing an ellipse is generally used  when (i) the major axies and minor axis are known, and (ii) the major axis and the distance between the foci are know.   Themethod of drawing the ellipse by the arcs of circle method is as follows and is shown in figure 7.

Draw AB & CD perpendicular to each other as the major diameter minor diameter respectively.
With centre as C or D, and half the major diameter as radius draw arcs to intersect the major diameter to obtain the foci at X and Y.
Mark a number of points along line segment XY and number them. Points need not be equidistant.
Set the compass to radius B1 and  draw two arcs, with Y as center.  Set the compass to radius A1, and draw two arcs with X as center. Intersection points of the two arcs are points on the ellipse. Repeat this step for all the remaining points. Use the French curve to connect the points, thus drawing the ellipse.

 

Figure 7. Drawing an ellipse by arcs of circle method.