# Find Parametric Equation for Moving Particle

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• October 11th 2010, 08:04 AM
lindsmitch
Find Parametric Equation for Moving Particle
Hello. I am familiar with parametric equations but the way this one is being asked is throwing me off.

Find parametric equations for the path of a particle that moves along the circle
(x-1)^2 + (y+2)^2 = 4 three times clockwise, starting at point (1,-4).
• October 11th 2010, 08:05 AM
Jhevon
Quote:

Originally Posted by lindsmitch
Hello. I am familiar with parametric equations but the way this one is being asked is throwing me off.

Find parametric equations for the path of a particle that moves along the circle
(x-1)^2 + (y+2)^2 = 4 three times clockwise, starting at point (1,-4).

i assume you know the (counter-clockwise) way to parameterize a circle, just do it the other way. you then want to choose the angle so that you get 3 revolutions out of it, beginning at the indicated point. How's that?
• October 11th 2010, 08:37 AM
Soroban
Hello, lindsmitch!

Quote:

$\text{Find parametric equations for the path of a particle}$
$\text{that moves along the circle: }\:(x-1)^2 + (y+2)^2 \:=\: 4$
$\text{ three times clockwise, starting at point (1, -4)}$

The path is a circle, center (1,-2) and radius 2.
The curve starts at "6 o'clock" and moves clockwise for 3 revolutions.

There is a variety of ways to write the parametric equations.
. . I'll use the easiest way (for me).

. . $\begin{Bmatrix}{x &=& 1 + 2\cos\theta \\ y &=& \text{-}2 + 2\sin\theta \end{Bmatrix}\quad \text{ for }\,\theta = \frac{3\pi}{2}\,\text{ to }\,\theta = \text{-}\frac{9\pi}{2}$
• October 11th 2010, 08:59 AM
lindsmitch
Thank you both very much. That was very helpful.

In the future, how would I have arrived at those parametric equations Soroban? Did you just use the conversion x = r * cos(theta) and y = r*sin(theta)?