construct a ellipse with distance of the focus from the dirctrix as 60 mm and eccentricity as 2/3 also draw normal and tangent to the curve at a point 40 mm from the directrix
Answers
Drawing ellipse by eccentricity method
1. Draw a horizontal line as shown Construct an ellipse when the distance of the focus from its Directrix 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 2030 Mark a point on horizontal line 20 mm from F as shown o
7. F 2030 Name the point as v as shown V o
8. FV Draw a line at V equal to VF as shown o
9. FV 1 o Mark the point as 1 as shown
10. FV 1 o JOIN O1 and extend as shown
11. 450FV 1 o Draw a line 450 to horizontal line from F and mark point P when it cuts the extended line of O1 P
12. FV 1 o P Draw a vertical line from F and mark the point 2 as shown 2
13. FV 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. FV 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. FV 1 o P 2 eM N 3 Mark point 3 such that MN=F3
16. FV 1 P 2 eM N 3 Join V23 by smooth curve as shown o
17. FV 1 P 2 eM N 3 Draw mirror image of the curve as shown o
18. FV 1 P 2 eM N 3 Draw mirror image of the curve as shown o
19. DAW LINES AS SHOWN as shown FV 1 P 2 eM N 3 o
20. FV 1 P 2 eM N 3 Mark the Points as shown o
21. FV 1 P 2 eM N 3 o Locate a point s as per given dimension to draw tangent and normal as shown s
22. FV 1 P 2 eM N 3 o s Join F S as shown
23. FV 1 P 2 eM N 3 o s Draw a line QF perpendicular to FS as shown Q
24. FV 1 P 2 eM N 3 o s Draw a line QQ’ Joining QS as shown Q Q’
25. FV 1 P 2 eM N 3 o s Draw a line NN’ Through S perpendicular to QQ’ as shown Q Q’ N’ N
26. FV 1 P 2 eM N 3 o s Q Q’ N’ N Ellipse Normal
Answer:
To calculate the value of a, use the formulas for the focus distance from the centre and the directrix distance from the centre. Determine the value of b now. You may extract the ellipse equation from this and plot it.
Explanation:
The directrix is represented by the vertical line DD. Draw a line parallel to the directrix at any point C on it to represent the axis CC'. The directrix and focus are separated by 60 mm. As a result, the focus is marked F1, with CF1=60mm. e=2/3. Create a right-angled CXY so that XY/CX = 2 units and 3 units. (X can be any point along the axis.) Draw a 45° line starting at F1 to cut CY at S. To intersect CF1 at V1, the vertex, extend S vertically. SV1 now equals F1V1. Draw a second line at a 45-degree angle from F1 to intersect CY's extension at T. To intersect the axis at V2, another vertex, extend vertically from T. Major Axis: V1V2. Mark points 1, 2,...., 10 at roughly equal intervals along the primary axis. Create vertical lines across these points that will intersect CY (made as needed) at 1′, 2′,..., and 10′. Draw two arcs on either side of the axis to cross the vertical line through 1 at P1 and P1′ using 11′ as the radius and F1 as the centre. Draw two arcs on either side of the axis to cross the vertical line drawn through 2 at P2 and P2′ using 22′ as the radius and F1 as the centre. Repeat the process above to get P3 and P3′,....,P10 and P10′, which stand in for 2,3,....,10 and P10, respectively. A smooth circle should be drawn through V1,P1,...,P10,V2,P10′,...,P1′,V1.
Mark F2 on the axis so that V2F2 = V1F1 to designate another Focus F2. Another Directrix "D" for you: Place a marker along the axis at C' so that C'V2 = CV1. Draw the vertical line D'D' through C'.
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