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The Fundamentals of Conic Sections

Learn how to craft geometric constructions and build conic sections in this free online technical drawing course.

Publisher: NPTEL
This free online course teaches you the key techniques used to draw basic geometric constructions and how to use these techniques to draw more complicated shapes called ‘conic sections’, which include parabolas, circles, ellipses and hyperbola. This course is for those who have a grounding in technical drawing and would like to apply their knowledge to engineering or 3D-modelling.
The Fundamentals of Conic Sections
  • Duration

    6-10 Hours
  • Students

  • Accreditation






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This course covers the technical drawing techniques used in the construction of all forms of conic section. We begin with the most basic geometric constructions used in engineering drawing: the bisection of a straight line, the bisection of an angle and the perpendicular bisector. These form the basis of conic sections and are followed by more challenging drawing techniques. We explain how to construct a circle around three different points before tackling tangents: the straight lines that just touch curves at a point. We cover common tangents as well as the interior and exterior tangents of a circle. These constructions are slightly more advanced and will need more focus and practice. We then move on to conic section fundamentals and the methods employed to construct them.

A geometric conic section is any curve produced by the intersection of a plane and a right circular cone. Depending on the angle of the plane relative to the cone, the intersection is a circle, an ellipse, a hyperbola or a parabola. These four shapes form the basis for all the construction methods studied in this course. We also outline four main methods used to construct the different shapes of a conic section, starting with the ‘focus-directrix method’. Then comes the ‘concentric circle method’, ‘oblong method’ and ‘arcs of circle method’. These four methods are capable of constructing all conics. The course then explains specific parabola constructions and demonstrates how to use the ‘rectangle method’. We also teach you how to use the ‘tangent method’ for parabola construction before moving on to special curves.

We examine various special curves, including cycloid curves, involutes, helixes and spirals. We show you how to construct each of these curves and unpack their different daily uses. The course takes you through the construction of the conical helix and a tangent to a spiral. The constructions covered in this course provide you with the basis for all engineering drawing construction and allow for the most accurate and disciplined drawing techniques. There is some equipment that can enable you to reap the full benefit of this course but it will not be needed for the final assessment. This course suits anyone looking to build on their knowledge of technical drawing while learning new techniques or those seeking a basic understanding of a foundational feature of all engineering careers. Sign up to pursue a path in the fields of engineering and technical drawing.

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