Introduction to Conics Sections

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In this lesson in our Math resources series, we discuss conics formulas or sections.  Conic sections are plane curves obtained by intersecting the planes in a cone.  The ancient Greeks revered these curves and, in fact, were written extensively by both Appolonius and Euclid.  Today, conics formulas remain highly important because of their many diverse applications in modern mathematics.

Although the layman might conjure up an image of a figure with a round base and pointed top, a mathematician’s idea of a cone is a surface that is obtained in a very precise way.

How a cone is formed

Imagine a vertical and another line intersecting it at an angle f (phi).  The vertical line is called the axis and the intersecting line is the generator.  The angle f (phi) created between the two lines is called the “vertex angle”. 

Now, use your imagination and imagine grasping the axis between forefinger and thumb on either side of the intersection point with a generator, and start twirling it.  The resulting surface is called a “cone”.

While conic formulas are visually appealing, their definitions for the conic sections tell students little about their uses and property.  Thus, one should strive to master their “plane geometry” definitions, as well.

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