chapter  9
Pages 9

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. See Figure 9.1. Conic sections: three types of curves formed by the intersection of a plane and a cone. From left to right: ellipse, parabola, and hyperbola.