# Thread: Find Parametric Equation for Moving Particle

1. ## 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).

2. 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?

3. Hello, lindsmitch!

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

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).

. . $\displaystyle \begin{Bmatrix}{x &=& 1 + 2\cos\theta \\ y &=& \text{-}2 + 2\sin\theta \end{Bmatrix}\quad \text{ for }\,\theta = \frac{3\pi}{2}\,\text{ to }\,\theta = \text{-}\frac{9\pi}{2}$

4. 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)?