The Parallelogram Method of Constructing Ellipses

Ellipse Construction, ContinuedParallelogramThe parallelogram method of constructing ellipses inscribes the ellipse withinellipsesa parallelogram. You may use conjugate diameters or the major and minoraxes to formulate the parallelogram so long as the sides of the parallelogramare parallel to the diameters or axes. step1ActionGiven the major and minor axes or the conjugate diameters AB andCD, draw a rectangle or parallelogram . Make sure all sides are parallel to their respective sides.
2Divide the distance between AO and AJ into the same number ofequal parts.
3Starting at the ends of the minor axis CD, lightly draw straight linesthrough each point. The lines intersect forming the circumferenceof the ellipse.
4Lightly sketch the outline of the ellipse. Darken the outline usingfrench curves.
To draw an ellipse by the parallelogram method, use this table;

Focus-Directrix orEccentricityMethod
Given :the distance offocusfrom the directrix and eccentricity
Example : Draw an ellipse if the distance of focus from the directrix is 70 mm and the eccentricity is 3/4.
1. Draw the directrix AB and axis CC’
2. Mark F on CC’ such that
CF= 70 mm.
3. Divide CF into 7 equal parts and mark V at the
3
parts and mark V at the fourth division from C.
Now, e = FV/ CV = 3/4.
4. At V, erect a perpendicular
VB = VF. Join CB. Through
F, draw a line at 45°to meet
CB produced at D. Through
D, drop a perpendicular
DV’ on CC’. Mark O at the midpoint of V– V’.Focus-Directrix orEccentricityMethod ( Continued)
5. With Fas a centre and radius =
1–1’, cut two arcs on the perpendicular through 1 to locate P1 and P1’. Similarly, with F as centre and radii = 2–
2’, 3–3’, etc., cut arcs on the corresponding perpendiculars to locate P2 and P2’, P3 and
P3’, etc. Also, cut similar arcs on the perpendicular through
4
on the perpendicular through
O to locateV1 and V1’.
6. Draw a smooth closed curve passing through V, P1, P/2, P/3,
…, V1, …, V’, …,