THE ELLIPSE

The Ellipse Figure 1 is ellipse. Distance AB and CD are major and minor axes respectively. Half of the major axis struck as a radius from D or C will give the foci F1 and F2. From a vertex E draw lines to F1 and F2. Bisect the angle at E. This bisector is called a normal. A line at right angles to the normal, touching the circumference at E is called a tangent.

To construct an ellipse given the lengths of the major and minor axes From centre O draw two circles equal in diameter to the given axis. Divide both circles into twelve equal parts and number as shown. Drop vertical lines from the point on the major diameter to intersect with horizontal lines drawn from the points on the minor diameter. A smooth curve passing through these intersections and the points A,B,3,8 will give the required ellipse. Figure 2 auxiliary circle method.

To Construct an ellipse using the trammel method given major & minor axes Draw major and minor axes DE and FG. On a strip of thin card (the trammel), mark AB equal to half the minor axis and AC equal to half the major axis. Move the trammel, keeping B always on the major axis and C always on the minor axis. Point A will trace out a path called a locus which will be an ellipse. Pencil lead could be fixed at A to give Figure 3.

To draw an approximate ellipse given the major & minor axes Draw the axes AB and CD. Divide each half of the major axis into two equal parts, marking R1 and R2. With R1 and R2 as centers, radius R1A draw circles. Through R1 and R2 draw lines inclined at 60 degrees to AB, extending to intersect the minor axis CD produced at R3 and R4.

With R3 as centre, radius R3C draw an arc and with R4 as centre, same radius, draw an arc. These arcs will join with the two circles to form an approximate ellipse- Figure 4.