Drawing ellipse by eccentricity method

1. Draw a horizontal line as shown Construct an ellipse when the distance of the focus from its D irectrix is equal to 50mm and eccentricity is 2/3.Also draw z tangent and a normal to the ellipse

2. Draw a vertical line line as shown(Directrix)

3. Mark the point as o as shown o

4. 50 Mark a point 50mm from vertical line on horizontal line as shown o

5. 50 Name the point as F(Focus) as shown F o

6. F 20 3 Mark a point on horizontal line 20 mm from F as shown o

7. F 20 3 Name the point as v as shown V o

8. F V Draw a line at V equal to VF as shown o

9. F V 1 o Mark the point as 1 as shown

10. F V 1 o JOIN O1 and extend as shown

11. 45 F V 1 o Draw a line 45 to horizontal line from F and mark point P when it cuts the extended line of O1 P

12. F V 1 o P Draw a vertical line from F and mark the point 2 as shown 2

13. F V 1 o P 2 Draw a vertical line from Point P to the horizontal line as shown and mark the point as e e

14. F V 1 o P 2 e Draw a bisector line for V e as shown and mark the point as M and N as shown M N = =

15. F V 1 o P 2 e M N 3 Mark point 3 such that MN=F3

16. F V 1 P 2 e M N 3 Join V23 by smooth curve as shown o

17. F V 1 P 2 e M N 3 Draw mirror image of the curve as shown o

18. F V 1 P 2 e M N 3 Draw mirror image of the curve as shown o

19. DAW LINES AS SHOWN as shown F V 1 P 2 e M N 3 o

20. F V 1 P 2 e M N 3 Mark the Points as shown o

21. F V 1 P 2 e M N 3 o Locate a point s as per given dimension to draw tangent and normal as shown s

22. F V 1 P 2 e M N 3 o s Join F S as shown

23. F V 1 P 2 e M N 3 o s Draw a line QF perpendicular to FS as shown Q

24. F V 1 P 2 e M N 3 o s Draw a line QQ’ Joining QS as shown Q Q’

25. F V 1 P 2 e M N 3 o s Draw a line NN’ Through S perpendicular to QQ’ as shown Q Q’ N ’ N

26. F V 1 P 2 e M N 3 o s Q Q’ N ’ N Ellipse Normal Tangent