Precalculus with Integrated CalculusXYZ Homework Edition

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Chapter 8: The Conic Sections

In this chapter, we study the Conic Sections - literally `sections of a cone'. Imagine a double-napped cone as seen below being `sliced' by a plane.

Image: cone
Figure 8.1

If we slice the cone with a horizontal plane the resulting curve is a circle.

Image: Circle01
Figure 8.2
Image: Circle02
Figure 8.3

Tilting the plane ever so slightly produces an ellipse.

Image: Ellipse01
Figure 8.4
Image: Ellipse02
Figure 8.5

If the plane cuts parallel to the cone, we get a parabola.

Image: Parabola01
Figure 8.6
Image: Parabola02
Figure 8.7

If we slice the cone with a vertical plane, we get a hyperbola.

Image: Hyperbola01
Figure 8.8
Image: Hyperbola02
Figure 8.9

If the slicing plane contains the vertex of the cone, we get the so-called `degenerate' conics: a point, a line, or two intersecting lines.

Adapted from Precalculus, Preliminary 4th Edition (integrated calculus), by Carl Stitz and Jeff Zeager (stitz-zeager.com), licensed under CC BY-NC-SA 3.0. Changes were made: reformatted as an accessible XYZ web edition. License: CC-BY-NC-SA-3.0.

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