Construct An parabola When The Distance Between The Focus And The Directrix Is 40mm

A. Construct An parabola When The Distance Between The Focus And The Directrix Is 40mm.Draw the tangent and normal at any point P on the curve using Directrix.

1. If The Eccentricity (e) is <1, the curve obtained is called Ellipse If The Eccentricity (e) is =1, the curve obtained is called Parabola If The Eccentricity (e) is >1, the curve obtained is called Hyperbola

2. A. Construct An parabola When The Distance Between The Focus And The Directrix Is 40mm.Draw the tangent and normal at any point P on the curve using Directrix.

3. Draw the axis AB

4. A B

5. Draw the Directrix CD at right angles to it:

6. A B C D

7. Mark the focus F on the axis at 50mm.

8. A B C D F 50MM

9. Locate the vertex V on AB such that AV = VF 25/25=1

10. A B C D F 50MM V

11. Draw a line VE perpendicular to AB such that VE = VF

12. A B C D F 50MM V E

13. . Join A,E and extend. Now, VE/VA = VF/VA = 1, the eccentricity.

14. A B C D F 50MM V E

15. Locate number of points 1,2,3, etc., to the right of V on the axis, which need not be equidistant .

16. A B C D F 50MM V E 1 2 4 3 5 6 7 8 10 9 11 12 13

17. Through the points 1,2,3, etc., draw lines perpendicular to the axis and to meet the line AE extended at 1',2',3' etc.

18. A B C D F 50MM V E 1 2 4 3 5 6 7 8 10 9 11 12 13 1’ 2’ 3’ 4’ 5’ 6’ 7’ 8’ 9’ 10’ 11’ 12’ 13’

19. With centre F and radius 1-1, draw arcs intersecting the line through I at P I and P II.

20. A B C D F 50MM V E 1 2 4 3 5 6 7 8 10 9 11 12 13 1’ 2’ 3’ 4’ 5’ 6’ 7’ 8’ 9’ 10’ 11’ 12’ 13’ P1

21. Similarly, lolcate the points P2 , P2 1, P3 , P/, etc., on either side of the axis. Join the points by smooth curve, forming the required parabola.

22. A B C D F 50MM V E 1 2 4 3 5 6 7 8 10 9 11 12 13 1’ 2’ 3’ 4’ 5’ 6’ 7’ 8’ 9’ 10’ 11’ 12’ 13’ P1 P1’ P2 P2’