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Precalculus with Limits: A Graphing Approach, Sixth Edition
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Precalculus with Limits: A Graphing Approach, Sixth Edition View details
Review Exercises
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Exercise 1 Page 700

A conic section is the intersection of a plane and a double-napped cone.

Hyperbola

Let's examine the intersections a double-napped cone and a plane for a parabola, circle, hyperbola, and ellipse.

Notice that the absolute value of the differences of the distances from two fixed points, called the foci, is constant. This means that the conic is a hyperbola. To get a hyperbola we slice through the double cone. The slice must be steeper than that for a parabola, but does not have to be parallel to the cone's axis for the hyperbola to be symmetrical.

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