Description
An Ellipse is a Conic Section and has the appearance of a circle which has been squashed slightly. Unlike a circle, which has a single Diameter, the ellipse has a Major Axis and a Minor Axis. The shape of an ellipse is sometimes mistakenly referred to as an oval, but an oval is the shape of a rectangle with two semicircular ends  like a running track for example.
The ellipse has two points of focus, or foci. These can be found on the Major Axis by using half its length as a radius, and striking an arc centred on one end of the Minor Axis as shown.
Constructions
Drawing an Ellipse using Concentric Circles

 Draw two circles from the same centre: one with its diameter equal to the Major Axis, and one equal to the Minor Axis.
 Divide the circles into a number of segments (say, 12 as shown).
 Project vertically from where the radial lines intersect the outer circle and .horizontally from where they meet the inner circle (or vice versa)
 Points on the ellipse can be found where each pair of projection lines meet as shown.
 Sketch a fair curve through the points (or use French Curves or a flexible strip for example)


Drawing an Ellipse using a loop of string

 A property of the ellipse is that the sum of the distances from any point on the curve to each of its two Foci is constant.
 Start by setting compasses, or similar, to half the Major Axis and strike arcs on it from one end of the Minor Axis as shown.
 The intersections found by the two arcs are the Focii of the ellipse.
 Place the drawing on a board and insert pins at each Foci then make a loop of string to go around them and reach the end of the Minor Axis when pulled tight.
 Hold a pencil inside the loop and keep the string tight as the pencil is pulled around to draw the complete ellipse as shown.


Note:
Ellipses may also be drawn by more precise methods and with Tangents and Normals drawn if needed  see Conics for more details.