Ellipses

Several methods are available of which the foci method (345:3) is the most common. The major axis which is to be the larger diameter of the ellipse is drawn first, and the minor axis at right angles to it. Focal points (foci) are then found by taking half the length of the major axis, and from point A on the minor axis striking an arc to cut the major axis at the foci Fl and F2. If pins

HYPERBOLA

345 Conic sections, ellipses, etc.

are inserted at A, Fl and F2 and a length of string stretched taut round them, with pin A removed and replaced by a pencil the curve can be traced by keeping the pencil taut against the string. Another familiar method (354:4) uses a trammel composed of a thin lath or strip of stout paper. The major and minor axes are drawn as before, the trammel is then marked with half the length of the major axis AB and half the minor axis BC, and if the point C is kept on the former and the point A on the latter then the point B will trace out the ellipse.

Ellipses can also be constructed by the rectangle method (345:5), in which both major and minor axes are divided into the same number of equal parts, and lines drawn through each division will yield points through which the

F1

1 1

F2

3

_____"""*

1 1 1

\

V I X \t

/

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