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Discussion

The arcs of circles method of drawing an ellipse uses the property that

  • A.the difference of distances to the two foci is constant
  • B.each point is equidistant from focus and directrix
  • C.the product of the distances to the axes is constant
  • D.the sum of distances to the two foci is constant

Answer: D

Correct answer: the sum of distances to the two foci is constant

This is the focal definition of the ellipse, and the arcs of circles method uses it directly: divide the major axis at a series of points, and from each strike arcs of the two complementary radii from the two foci to locate points on the curve. It is the same property the gardener’s loop of string exploits.

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