The geometric definition suggests a simple method for drawing an ellipse. Place a
sheet of paper on a drawing board, and insert thumbtacks at the two points that are to
be the foci of the ellipse. Attach the ends of a string to the tacks, as shown in Figure
2(a). With the point of a pencil, hold the string taut. Then carefully move the pencil
around the foci, keeping the string taut at all times. The pencil will trace out an ellipse,
because the sum of the distances from the point of the pencil to the foci will always
equal the length of the string, which is constant.
FiguRE 2 (a) (b)
place the foci on the x-axis at F11c, 02 and F21c, 02 so that the origin is halfway beIf the string is only slightly longer than the distance between the foci, then the ellipse that is traced out will be elongated in
shape, as in Figure 2(a), but if the foci are close together relative to the length of the string, the ellipse will be almost circular, as
shown in Figure 2(b).
CHAPTER 1 ■ Conic Sections
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