Associated Topics || Dr. Math Home || Search Dr. Math

### 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

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/
```
Associated Topics:
High School Conic Sections/Circles
High School Equations, Graphs, Translations
High School Geometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search