SPECIAL CURVES I (CONT’D)

ELLIPSE CONSTRUCTION (CONT’D)

C. CIRCLE ( AUXILIARY/CONCENTRIC CIRCLES) METHOD

Given
Major Axis= 80
Minor Axis= 60

Procedure

1. Draw the two concentric circles using the given radii.
2. Divide the big circle into number of equal parts(say 12).
3. Draw vertical lines from all the divisions 1 – 12.
4. Draw horizontal lines from the points of intersection of radiating lines 1 – 12 and the inner circle to intersect with the vertical lines.
5. Join their points of intersection to get the ellipse.

D. TRAMMEL METHOD
Given
Major Axis= 100
Minor Axis= 60

Procedure

1. Draw the two axes XZ and WY at right angles to each other.
2. Mark the trammel with a pencil so that half the major and minor axes are narked from the same point P( check the diagram for this).
3. Keep B on the minor axis, A on the major axis and slide the trammel, marking the position of P at frequent intervals.
   Point P will trace an ellipse.

E. TO DRAW A TANGENT AND A NORMAL TO AN ELLIPSE AT A GIVEN POINT ON THE CIRCUMFERENCE

Procedure

1. Draw the given ellipse with the major and minor axes AB and CD respectively.
2. Locate the given point P on the circumference.
3. Locate the focal points F1 and F2 with centre at C, radius OA.
4. Join PF1 and PF2.
5. Bisect angle F1PF2. The bisector is the normal.
6. Construct a perpendicular to the normal at P to get the tangent.