s is to use a flashlight and have an empty wall in your house. By holding the flashlight parallel to the floor, you will produce a circle on the wall. In holding the flashlight slightly tilted, an ellipse is formed. When you hold the flashlight so that the side farthest away from the wall is parallel to the wall, a parabola is formed. Finally, when the flashlight is tilted so that it is almost parallel to the floor, you will get half of a hyperbola because the flashlight can only simulate a single cone, as the wall represents the plane. (West, 114-115)To get into the details of conic sections it is necessary to break them up into each separate conic section. The circle can be considered the simplest conic section because it is the easiest to understand. A Greek Philosopher named Apollonius was studying the first forms of the circle back around 225 B. C., while he was writing Conic Sections, which was a series of eight different books analyzing all the primate forms of these shapes. (West, 113) This was around when someone, not necessarily him, noticed that when the circumference of any circle was divided by the diameter, a similar number, or a constant, somewhere around 3 was always achieved. There are even references to this found in the bible describing some sort of circular container that held a large amount of water. Well, over 2,000 years later, we use the formula C=D. That is how we would normally come up with the circumference of a circle with either the diameter or the radius (doubled equals the diameter) given. To apply the circle in conic sections, it should be used as a locus of points equal distance from a given point to show how the formulas are derived. Knowing that, the radius is the given distance, and the center of the circle is the point from which the circumference is equal distance of. On a graph, with the center at the origin, one would take any point on the circumference of the circle, (x,y), to get ...
