---------------------Geometrical Contructions 4.19
- Repeat steps 3 to 5 to obtain the points in the remaining three quadrants.
- Join the points by a smooth curve forming the required ellipse.
To draw an ellipse passing through any three given points not in a line.
Construction (Fig. 4.28)Fig. 4.28- Locate the given points A,B and C
- Join A and B (which is longer than AC and BC) and locate its centre. This becomes the
major axis of the ellipse. - Draw CO and extend it to D such that CO = OD and CD is the minor axis of the ellipse.
- Draw the parallelogram KLMN, Passing through A,D,B and C.
- Follow the"steps given is FigA.27 and obtain the points on the curve.
- Join the points by a smooth curve, forming the required ellipse.
- Concentric Circles Method (Fig. 4.29)
- Draw the major and minor axes AB and CD and locate the centre O.
- With centre 0 and major axis and minor axes as diameters, draw two concentric circles.
- Divide both the circles into equal number of parts, say 12 and draw the radial lines.
- Considering the radial line 0-1' -1, draw a horizontal line from I' to meet the vertical line
from 1 at Pl' - Repeat the steps 4 and obtain other points P 2 , P 3 , etc.
- Join the points by a smooth curve forming the required ellipse.
- Trammel Method (Fig.4.30)
- Draw the major and minor axes AB and CD and then locate the centre O.
- Take.a strip of stiff paper and prepare a trammel as shown. Mark the semi-major and
semi-minor axes PR and PQ on the trammel.