Non-Algebraic Explanation of a Parabola
Date: 05/18/2000 at 09:09:25 From: Donelle Subject: Parabola I need to know specific details about a Parabola in more simple words. They can be math words but more simple, please. Thank you.
Date: 05/18/2000 at 12:05:24 From: Doctor Peterson Subject: Re: Parabola Hi, Donelle. Okay, I'll give it a try. I love putting math into simple terms, but it's very hard to do that when I don't know what you need. The more you can tell me about your needs, the better I can help. First, let me point you to a page in our archives that I think you might find useful as a starter, since it's written for a younger student and avoids algebra: An Introduction to Parabolas http://mathforum.org/dr.math/problems/hayley2.4.99.html A parabola can be defined in several ways. First, it is a conic section; if you take a cone and cut a slice off parallel to its slope, like this, the curve you get will be a parabola: /\ /\/ \cutting plane / /\ \ / / \ \ / / \ \ / / \ \ / / * * \ / / * /*\ \ / / * / * \ \ parabola-------->* / * \ / / / s/ * \/ / / * i/ /\ / / x/ * / \ / \ * a/ / \cone / \ / * / \ / ++*+++/++++++++/++++ \ /+++++ \ / * / +++++\ + + * / + ++++++ \ * / ++++++ ++++++*++++/++++++++ \ / \/ Second, it can be defined in terms of the "focus" and "directrix." We choose a point in a plane that will be the focus, and a line (usually parallel to the x- or y-axis, but it could be any line) for the directrix. The parabola is the set of all points that are the same distance from the focus as from the directrix. Since the distance from a point to a line is the distance along the perpendicular, that looks like this: * * Focus * + * \ a \ * * P * | |b | -------------------------------+--------------- Directrix The distance a from the focus to point P is the same as the distance b from point P to the directrix, so P is on the parabola. If you want a better picture, look at the page Dr. Rick referred to in his archived answer. Dave's Math Tables: Conic Sections - David Manura http://math2.org/math/algebra/conics.htm Now, you can use this definition to derive the equation of a parabola. I won't get into that, because once we do that, I can't avoid digging into algebra. If you want to know how to write the equation, or how to find the focus and directrix from the equation, and so on, please write back and tell me what you need to know. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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