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 semi-circular 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
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- 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)
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| Drawing an Ellipse using a loop of string
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- 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.
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Note:
Ellipses may also be drawn by more precise methods and with Tangents and Normals drawn if needed - see Conics for more details.
