Constructing the Ellipse
≈ 36 minConstructing the Ellipse
An ellipse appears whenever a circle is viewed at an angle — which is constantly, in isometric drawing and in any inclined circular face. It has a major axis (longest diameter) and a minor axis (shortest), always perpendicular and crossing at the centre.
The concentric-circle method (CAPS Grade 10). Draw two circles about the same centre: one on the major axis as diameter, one on the minor. Draw radial lines out from the centre. Where a radial cuts the outer circle, drop a vertical; where the same radial cuts the inner circle, draw a horizontal. Their crossing is a point on the ellipse. Repeat for a dozen radials and join with a smooth curve.
Worked example. Twelve radials give twelve points — enough for a smooth curve. Four points produce a shape that visibly kinks between them, and the eye reads it as a badly drawn oval rather than an ellipse.
Core checkpoint: Take the vertical from the outer circle and the horizontal from the inner one. Swapping them gives a valid-looking curve that is the wrong ellipse.
In the concentric-circle method, how is one point on the ellipse found?
What is the name of the longest diameter of an ellipse?
Why is an ellipse drawn as two semicircles joined by flatter curves not acceptable?
A learner takes the horizontal from the outer circle and the vertical from the inner circle — the opposite way round. What is the result?