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Mastering Engineering Graphics: Conic Sections Demystified

This comprehensive guide covers dividing a line into unequal segments, ellipse, parabola, hyperbola, and tangent and normal to conics. Learn to draw ellipses using major and minor axes effectively.

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Mastering Engineering Graphics: Conic Sections Demystified

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  1. Anjuman College of Engineering & Technology EngineeringGraphics -I Unit-I Prof. Ravindra R Paliwal Department of Mechanical Engineering

  2. Dividealineinnequalsegments.

  3. Dividealineinnequalsegments.

  4. Dividealineinnequalsegments.

  5. Dividealineinnequalsegments.

  6. Dividealineinnequalsegments.

  7. ConicSections distanceof thepointfromthefocus Eccentricity= distanceof thepointfromdirectrix e<1⇒Ellipse,e=1⇒Parabolaande>1⇒Hyperbola.

  8. ConicSections Anellipse⇒Section plane AA,inclinedtothe axiscuts allthe generatorsofthe cone. 1 Aparabola⇒Section plane BB,parallel tooneofthe generatorscuts the cone. 2 Ahyperbola ⇒Section plane CC,inclinedtothe axiscuts the coneonone sideofthe axis. 3 Arectangularhyperbola ⇒ Section plane DD,parallel tothe axiscuts the cone. 4

  9. EllipsebyDirectrixandFocus e=2/3 andfocusdistancefromdirectrixisknown. DivideCFinfiveequal segments.DrawVE⊥CF and VF=VE. 1

  10. EllipsebyDirectrixandFocus e=2/3 andfocusdistancefromdirectrixisknown. DivideCFinfiveequal segments.DrawVE⊥CF and VF=VE. 1 Extend CEtocoverthe horizontal span ofthe ellipse. 2

  11. EllipsebyDirectrixandFocus e=2/3 andfocusdistancefromdirectrixisknown. DivideCFinfiveequal segments.DrawVE⊥CF and VF=VE. 1 Extend CEtocoverthe horizontal span ofthe ellipse. 2 Drawavertical at 1. 3

  12. EllipsebyDirectrixandFocus e=2/3 andfocusdistancefromdirectrixisknown. DivideCFinfiveequal segments.DrawVE⊥CF and VF=VE. 1 Extend CEtocoverthe horizontal span ofthe ellipse. 2 Drawavertical at 1. 3 Usethe compass tomeasure 11‘ and mark P1 and P‘ 4 1 fromF.

  13. EllipsebyDirectrixandFocus e=2/3 andfocusdistancefromdirectrixisknown. DivideCFinfiveequal segments.DrawVE⊥CF and VF=VE. 1 Extend CEtocoverthe horizontal span ofthe ellipse. 2 Drawavertical at 1. 3 Usethe compass tomeasure 11‘ and mark P1 and P‘ 4 1 fromF. Anypoint,P2 orP0,isC2distanceapartfromthedirectrixandFP2 2 orFP0 apartfromthefocus. 2

  14. EllipsebyDirectrixandFocus e=2/3 andfocusdistancefromdirectrixisknown. DivideCFinfiveequal segments.DrawVE⊥CF and VF=VE. 1 Extend CEtocoverthe horizontal span ofthe ellipse. 2 Drawavertical at 1. 3 Usethe compass tomeasure 11‘ and mark P1 and P‘ 4 1 fromF. Anypoint,P2 orP0,isC2distanceapartfromthedirectrixandFP2 2 orFP0 apartfromthefocus. 2

  15. EllipsebyDirectrixandFocus e=2/3 andfocusdistancefromdirectrixisknown. DivideCFinfiveequal segments.DrawVE⊥CF and VF=VE. 1 Extend CEtocoverthe horizontal span ofthe ellipse. 2 Drawavertical at 1. 3 Usethe compass tomeasure 11‘ and mark P1 and P‘ 4 1 fromF. Anypoint,P2 orP0,isC2distanceapartfromthedirectrixandFP2 2 orFP0 apartfromthefocus. 2

  16. EllipsebyDirectrixandFocus e=2/3 andfocusdistancefromdirectrixisknown. DivideCFinfiveequal segments.DrawVE⊥CF and VF=VE. 1 Extend CEtocoverthe horizontal span ofthe ellipse. 2 Drawavertical at 1. 3 Usethe compass tomeasure 11‘ and mark P1 and P‘ 4 1 fromF. Anypoint,P2 orP0,isC2distanceapartfromthedirectrixandFP2 2 orFP0 apartfromthefocus. 2

  17. EllipsebyDirectrixandFocus e=2/3 andfocusdistancefromdirectrixisknown. DivideCFinfiveequal segments.DrawVE⊥CF and VF=VE. 1 Extend CEtocoverthe horizontal span ofthe ellipse. 2 Drawavertical at 1. 3 Usethe compass tomeasure 11‘ and mark P1 and P‘ 4 1 fromF. Anypoint,P2 orP0,isC2distanceapartfromthedirectrixandFP2 2 orFP0 apartfromthefocus. 2

  18. Tangent andNormalstoConics When atangentat any point onthe curveis produced tomeet the directrix, the linejoiningthe focuswiththismeeting point willbeat right angles tothe linejoiningthe focus withthe point ofcontact. 1

  19. Tangent andNormalstoConics When atangentat any point onthe curveis produced tomeet the directrix, the linejoiningthe focuswiththismeeting point willbeat right angles tothe linejoiningthe focus withthe point ofcontact. 1

  20. Tangent andNormalstoConics When atangentat any point onthe curveis produced tomeet the directrix, the linejoiningthe focuswiththismeeting point willbeat right angles tothe linejoiningthe focus withthe point ofcontact. 1

  21. Tangent andNormalstoConics When atangentat any point onthe curveis produced tomeet the directrix, the linejoiningthe focuswiththismeeting point willbeat right angles tothe linejoiningthe focus withthe point ofcontact. 1

  22. EllipsefromMajorandMinorAxis Drawmajor and minoraxes and twocircles. 1

  23. EllipsefromMajorandMinorAxis Drawmajor and minoraxes and twocircles. 1 Divideitforsufficientpoints todrawthe ellipse. 2

  24. EllipsefromMajorandMinorAxis Drawmajor and minoraxes and twocircles. 1 Divideitforsufficientpoints todrawthe ellipse. 2 Drawavertical at 1. 3

  25. EllipsefromMajorandMinorAxis Drawmajor and minoraxes and twocircles. 1 Divideitforsufficientpoints todrawthe ellipse. 2 Drawavertical at 1. Drawhorizontal at 1‘ 3 4

  26. EllipsefromMajorandMinorAxis Drawmajor and minoraxes and twocircles. 1 Divideitforsufficientpoints todrawthe ellipse. 2 Drawavertical at 1. Drawhorizontal at 1‘ Repeat the procedure described inthe last two steps 3 4 5

  27. EllipsefromMajorandMinorAxis Drawmajor and minoraxes and twocircles. 1 Divideitforsufficientpoints todrawthe ellipse. 2 Drawavertical at 1. Drawhorizontal at 1‘ Repeat the procedure described inthe last two steps 3 4 5

  28. EllipsefromMajorandMinorAxis Drawmajor and minoraxes and twocircles. 1 Divideitforsufficientpoints todrawthe ellipse. 2 Drawavertical at 1. Drawhorizontal at 1‘ Repeat the procedure described inthe last two steps 3 4 5

  29. EllipsebyOblongmethod DivideAOand AEinequal segments (4) 1

  30. EllipsebyOblongmethod DivideAOand AEinequal segments (4) Join1‘,2‘ and 3‘ toC 1 2

  31. EllipsebyOblongmethod DivideAOand AEinequal segments (4) Join1‘,2‘ and 3‘ toC Join1,2and 3withDand extend 1 2 3

  32. EllipsebyOblongmethod DivideAOand AEinequal segments (4) Join1‘,2‘ and 3‘ toC Join1,2and 3withDand extend 1 2 3 Onvertical P2P11 cut P2x=xP11 4

  33. EllipsebyOblongmethod DivideAOand AEinequal segments (4) Join1‘,2‘ and 3‘ toC Join1,2and 3withDand extend 1 2 3 Onvertical P2P11 cut P2x=xP11 Onhorizontal P2P5 cut P2y=yP5 4 5

  34. EllipsebyOblongmethod DivideAOand AEinequal segments (4) Join1‘,2‘ and 3‘ toC Join1,2and 3withDand extend 1 2 3 Onvertical P2P11 cut P2x=xP11 Onhorizontal P2P5 cut P2y=yP5 Findother point similarly 4 5 6

  35. EllipsebyOblongmethod DivideAOand AEinequal segments (4) Join1‘,2‘ and 3‘ toC Join1,2and 3withDand extend 1 2 3 Onvertical P2P11 cut P2x=xP11 Onhorizontal P2P5 cut P2y=yP5 Findother point similarly 4 5 6

  36. Parabolaforagivenfocusdistance Bisect CFforthe vertexV withproper process. 1

  37. Parabolaforagivenfocusdistance Bisect CFforthe vertexV withproper process. 1 Drawavertical at 1and cut FP‘ and FP1 =C1. 2 1

  38. Parabolaforagivenfocusdistance Bisect CFforthe vertexV withproper process. 1 Drawavertical at 1and cut FP‘ and FP1 =C1. 2 1 Repeat formorepoints. 3

  39. Parabolaforagivenfocusdistance Bisect CFforthe vertexV withproper process. 1 Drawavertical at 1and cut FP‘ and FP1 =C1. 2 1 Repeat formorepoints. 3

  40. Parabolaforagivenbaseandaxis Drawthe baseABand axis EFfrommidpoint E. 1

  41. Parabolaforagivenbaseandaxis Drawthe baseABand axis EFfrommidpoint E. 1 ConstructrectangleABCD and divideABand CDin equal parts. 2

  42. Parabolaforagivenbaseandaxis Drawthe baseABand axis EFfrommidpoint E. 1 ConstructrectangleABCD and divideABand CDin equal parts. 2 DrawlinesF1,F2,F3and perpendiculars1‘P1,2‘P2 and 3‘P3. 3

  43. Parabolaforagivenbaseandaxis Drawthe baseABand axis EFfrommidpoint E. 1 ConstructrectangleABCD and divideABand CDin equal parts. 2 DrawlinesF1,F2,F3and perpendiculars1‘P1,2‘P2 and 3‘P3. Cut points likeP‘.... 3 4 1

  44. Parabolaforagivenbaseandaxis Drawthe baseABand axis EFfrommidpoint E. 1 ConstructrectangleABCD and divideABand CDin equal parts. 2 DrawlinesF1,F2,F3and perpendiculars1‘P1,2‘P2 and 3‘P3. Cut points likeP‘.... 3 4 1

  45. ParabolainParrallelogram Followsimilarprocess.

  46. Hyperbolaforagiveneccentricity Followsimilarprocess.

  47. RectangularHyperbolathroughagivenpoint (e=√2and equationmaybeassumed asxy=1not x2−y2 =1) Drawthe axesOA,OBand mark point P. 1

  48. RectangularHyperbolathroughagivenpoint (e=√2and equationmaybeassumed asxy=1not x2−y2 =1) Drawthe axesOA,OBand mark point P. 1 DrawCDkOA,EFkOB. 2

  49. RectangularHyperbolathroughagivenpoint (e=√2and equationmaybeassumed asxy=1not x2−y2 =1) Drawthe axesOA,OBand mark point P. 1 DrawCDkOA,EFkOB. Markpoints 1,2,3... (may not beequidistant) 2 3

  50. RectangularHyperbolathroughagivenpoint (e=√2and equationmaybeassumed asxy=1not x2−y2 =1) Drawthe axesOA,OBand mark point P. 1 DrawCDkOA,EFkOB. Markpoints 1,2,3... (may not beequidistant) 2 3 JoinO1and 1P1 kOB and 1‘P1 kOAtofindP1 4

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