Conic Sections

(not in course)

A conic section is a curve formed by slicing through a cone. There are four different curves that are called conic sections:

Imagine a cone sitting flat on a table with its point (and its central axis) directly up.

A circle is formed by slicing horizontally through the cone (perpendicular to the axis). (No 2 in diagram)

An ellipse is formed by slicing through the cone at an angle to the horizontal but so that the slice only cuts through the curved surface of the cone. (No 2 in diagram)

A parabola is formed by slicing through the cone parallel to the sloping side of the cone. The slice will therefore cut through the end of the cone. (No 1 in diagram)

A hyperbola is formed by slicing vertically through the cone (parallel to the axis).

  • If a second cone is inverted and placed point-to-point above the first cone, a vertical slice will create the two halves of the hyperbola. (No 3 in diagram)


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