An Introduction to ParabolasDate: 02/04/99 at 22:31:54 From: Hayley Subject: Parabolas What is a parabola? I have heard my brother, who is in high school, use it. I need your help! Sincerely, Hayley Date: 02/05/99 at 12:59:24 From: Doctor Rick Subject: Re: Parabolas Hi, Hayley. Thanks for your question! I did a Web search and here is one nice page I found: Dave's Math Tables: Conic Sections - David Manura http://math2.org/math/algebra/conics.htm A parabola is a curve of a particular shape. You have seen parabolas when you watch a stream of water from a hose or fountain, starting upward, curving as it nears the peak, and straightening out somewhat as it heads back down. It's the path followed by any thrown object, but it's easiest to see with water. The path is called a "parabolic trajectory." You can understand some things about a parabola before you learn algebra. Parabolas were known long before algebra was invented. The Greek mathematician Apollonius wrote a book called "Conic Sections" that studied parabolas and related curves. A conic section is what you get if you take a cone and slice it with a plane. Look at the Web page above for some nice illustrations of this. If the plane is parallel to the side of the cone, you get a parabola. If the plane is in other directions, you get a circle, an ELLIPSE, or a HYPERBOLA. Parabolas have some interesting properties. If you draw a line and a point somewhere off the line, a parabola is the set of all the points in the plane that are the same distance from the point and the line. (Distances from a point to a line are measured perpendicular to the line.) . . . . . . . . . *---------------. . |\ . | . | \ . | . | \. | . | | | | | | | | | | | ------------------------------------------------------------ That * in the picture, the point you chose, is called the FOCUS of the parabola. The line is called the DIRECTRIX. If you make a mirror shaped like a parabola (a PARABOLIC MIRROR) and put a lightbulb at the focus, the light that reflects from the mirror will all be shining in the same direction - which is why flashlights have parabolic mirrors. You can run the same thing backward: light (or radio waves) coming toward a parabolic mirror from far away will all reflect in toward the focus - the light or radio waves are FOCUSED. Reflecting telescopes take advantage of this property of parabolas, and so do parabolic dish antennas for satellite TV and such. Parabolas are all over the place, and as you can see, they are important. But algebra makes it a lot easier to study and understand them. The equations that describe parabolas are called "quadratic equations." You'll learn a lot more about this when you get to algebra. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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