There are various methods in drawing an ellipse. We have the simple Pins & Strings method, the Concentric-circle method, and the Four-center method. I will share to you the Four-center method by giving the steps and a diagram so it will be easier to understand.
1. Draw the major axis, AB, and the minor axis, CD, which are mutually perpendicular at the midpoint, O, as shown in the diagram.
2. Draw AD, that connects the end points of the two axes.
3. Using a compass, point the tips of it to DO then plot it along AO and reset the compass on the remaining distance to O.
4. With the difference of semiaxes thus set on the dividers, mark off DE equal to AO minus DO.
5. Draw perpendicular bisector AE, and extend it to intersect the major axis at K and the minor axis at H.
6. With the compass, mark off OM equal to OK, and OL equal to OH.
7. With H as a center and radius R1 equal to HD, draw the bottom arc.
8. With L as a center and the same radius as R1, draw the top arc.
9. With M as a center and the radius R2 equal to MB draw the end arc.
10. With K as a center and the same radius as R2, draw the other end arc.
The four circular arcs thus drawn meet, in common points of tangency, P, at the ends of their radii in their lines of centers.
If you have questions or request, feel free to leave a comment.