7.1: Introduction to Conics

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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.

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

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Tilting the plane ever so slightly produces an ellipse.

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

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

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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.

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We will focus the discussion on the non-degenerate cases: circles, parabolas, ellipses, and hyperbolas, in that order. To determine equations which describe these curves, we will make use of their definitions in terms of distances.