Construction of Parabola by Tangent Method

CONSTRUCTION OF PARABOLA BY TANGENT METHOD 

Data known : 

1. Base 

2. Axis

Example 7: Construct a parabola with the length of base as 80mm and axis 40mm. Also draw a tangent and normal to the curve at a point 34 mm from the base.

Procedure:

1. Draw the base AB and draw its bisector through its mid point C.

2. Mark the points D and E on the bisector such that CD = DE = 40 mm.

3. Join E with A and B, Lines AE and BE are the tangents to the parabola at A and B respectively.

4. Divide the tangents AE and BE into same number of parts (say 6) and name the parts as 1, 2 etc., on AB from A and 1', 2' etc., on EB from E.

5. Join 1 and 1', 2 and 2' etc., which are the tangents to the required parabola...

6. Draw a smooth curve passing through the points A, D and B such that tangential to the above lines 1-1', 2-2' etc.,

To draw Tangent and normal

i) Locate a point M on the curve at a height of 34mm (given in problem) from base then draw a horizontal through M to meet the axis at F.

ii) On the axis mark a point G such that GD = DF. 

iii) Join G and M and extend which is the required TT' tangent at M.

iv) Draw a line NN' perpendicular to the tangent drawn, which is the required normal.