Chapter 19

Conics

Take a flashlight and shine it straight onto a wall. You will see a circle. Tilt the light, and the circle will turn into an ellipse. Tilt further, and the ellipse will become more and more elongated, and will become a parabola eventually. Tilt a little more, and you will have a hyperbola—actually one branch of it. The beam of your flashlight is a cone, and the image it generates on the wall is the intersection of that cone with a plane (i.e., the wall). Thus, we have the name conic section for curves that are the intersections of cones and planes. Figure 19.1 illustrates this idea.

Figure 19.1

Figure showing conic sections: three types of curves formed by the intersection of a plane and a cone. From left to right: ellipse, parabola, and hyperbola.

Conic sections: three types of ...

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