# parameterization

• May 23rd 2010, 03:12 PM
kevin11
parameterization
Find a parameterization for each of the following curves.

a. The straight line segment from (3,2) to (-1,1).
b. The curve $\displaystyle y=1-x^2$ from (3,-8) to (-2,-3).

I have no idea how to do this problem. Looks like a basic problem but I have no idea what parameterization means. Any help is appreciated!
• May 23rd 2010, 03:53 PM
dwsmith
Quote:

Originally Posted by kevin11
Find a parameterization for each of the following curves.

a. The straight line segment from (3,2) to (-1,1).
b. The curve $\displaystyle y=1-x^2$ from (3,-8) to (-2,-3).

I have no idea how to do this problem. Looks like a basic problem but I have no idea what parameterization means. Any help is appreciated!

a.
$\displaystyle x(t)=(t-1)\mathbf{i}, 0\leq t \leq 4$ From this equation, the line will move from -1 to 3 on the x axis.
$\displaystyle y(t)=\left(\frac{t}{4}+1\right)\mathbf{j}, 0\leq t \leq4$ From this equation, the line will move from 1 to 2 on the y axis.
$\displaystyle r(t)=(t-1)\mathbf{i}+\left(\frac{t}{4}+1\right)\mathbf{j}, 0\leq t \leq4$ $\displaystyle r(t)=x(t)+y(t)+z(t)$; $\displaystyle z(t)$ if in 3 dimensions.
• May 23rd 2010, 03:55 PM
kevin11
Quote:

Originally Posted by dwsmith
a.
$\displaystyle x(t)=(t-1)\mathbf{i}, 0\leq t \leq 4$
$\displaystyle y(t)=\left(\frac{3t}{4}+2\right)\mathbf{j}, 0\leq t \leq4$
$\displaystyle r(t)=(t-1)\mathbf{i}+\left(\frac{3t}{4}+2\right)\mathbf{j} , 0\leq t \leq4$

hey thanks for the reply! How did you come up with those? Are there some formulas you can show me that would help with these problems? I'm not finding anything in my textbook.
• May 23rd 2010, 03:56 PM
dwsmith
Quote:

Originally Posted by kevin11
hey thanks for the reply! How did you come up with those? Are there some formulas you can show me that would help with these problems? I'm not finding anything in my textbook.

I had a typo so I edited my last post.
• May 23rd 2010, 04:03 PM
kevin11
So what exactly is the question asking for? Sorry but I've never heard of parameterization, nor can I find it in the textbook.

Am I looking for an equation for these two points or..?
• May 23rd 2010, 04:05 PM
dwsmith
Quote:

Originally Posted by kevin11
So what exactly is the question asking for? Sorry but I've never heard of parameterization, nor can I find it in the textbook.

Am I looking for an equation for these two points or..?

Parametric Equations -- from Wolfram MathWorld
• May 23rd 2010, 04:13 PM
kevin11
Quote:

Originally Posted by dwsmith

Ok thanks for your help. I think I'll just skip this one for now.
• May 24th 2010, 04:27 AM
HallsofIvy
Quote:

Originally Posted by kevin11
Find a parameterization for each of the following curves.

a. The straight line segment from (3,2) to (-1,1).
b. The curve $\displaystyle y=1-x^2$ from (3,-8) to (-2,-3).

I have no idea how to do this problem. Looks like a basic problem but I have no idea what parameterization means. Any help is appreciated!

Then I assume you immediately looked up "parameterization" or "parameter" in the index of your book and now know what it means!

A parameter or a curve is an additional variable, t, say such that both x and y are written in terms of that variable. Any one-dimensional object, such as a curve, can be written in terms of 1 parameter, any two-dimensional object, such as a surface, can be written in terms of two parameters. In effect, that's what "dimension" means.

But as long as y is a function of x, we can use "x" itself as parameter.

If $\displaystyle y= 1- x^2$ we can take $\displaystyle x= t$, $\displaystyle y= 1- t^2$ with $\displaystyle -3\le t\le t$.