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

### Latus Rectum

```Date: 08/08/2002 at 16:17:39
From: Michelle
Subject: Latus rectum

Dr. Math,

I'm working on quadratic equations, and I'm trying to find the
definition, an explanation, a formula, or anything that will help me
to better understand what exactly latus rectum is. So far all I have
been able to find is that when using the formula (x-h)=4p(y-k), the
latus rectum is equal to 4p. I don't understand, and any explanation
would be wonderful!  Thank you.

Michelle
```

```
Date: 08/08/2002 at 23:36:18
From: Doctor Peterson
Subject: Re: Latus rectum

Hi, Michelle.

I would think your book would define the term; but then, I've just
been searching the Web for a picture of a parabola that shows the
latus rectum, and I can't seem to find any! It's so simple and visual,
there's no reason not to show it; I'll let you draw it yourself.

Just find a picture of a parabola that shows the focus and either the
axis or the directrix, or both. Now draw a line through the focus
that is parallel to the directrix (that is, perpendicular to the
axis). It will look something like this:

o            |F           o
--o-----------o-----------o--
A o          |         o  B
o      |      o
oV
|
|
--------------o-------------- d
D

The vertex is V(h,k), the focus is F, the axis is the line DF, the
directrix is the line d, and the line segment AB is the latus rectum,
which is Latin for "straight side." Its length is 4p in your equation

4p(y-k) = (x-h)^2

where p is the focal length DV=VF. That is, the semi-latus rectum FB
is the same length as FD. If you think about the definition of the
parabola, you will see why that has to be true.

Here is one of many pages that show a parabola, including the focus
and directrix, from Eric Weisstein's MathWorld:

http://mathworld.wolfram.com/Parabola.html

Here 'a' is used where you use 'p', so don't let that confuse you.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Calculus
High School Conic Sections/Circles

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