1. ## parametric equations

find parametric equations for the path of particle that moves along x2+(y-1)2=4 in a manner described.....

A.) once around clockwise, starting at (2,1)
B.) three times around counterclockwise, starting at (2,1)
C.) halfway around counterclockwise, starting at (3,0)

2. ## Re: parametric equations

Originally Posted by pnfuller
find parametric equations for the path of particle that moves along x2+(y-1)2=4 in a manner described.....

A.) once around clockwise, starting at (2,1)
B.) three times around counterclockwise, starting at (2,1)
C.) halfway around counterclockwise, starting at (3,0)

Since this is a circle, the Pythagorean Identity makes the parameterisations quite easy.

3. ## Re: parametric equations

Hello, pnfuller!

Find parametric equations for the path of particle that moves along $\displaystyle x^2 + (y-1)^2 \:=\:4$ in the manner described.
The equation represents a circle with center $\displaystyle (0,1)$ and radius $\displaystyle r =2.$
Code:
                |
* * *
*     |     *
*       |       *
*        |        *
|
*         |         *
*        1* - - - - o(2,1)
*         |         *
|
-----*--------+--------*-----
*       |       *
*     |     *
* * *
|
The parametric equations are: .$\displaystyle \begin{Bmatrix}x \;=\;2\cos\theta \\ y \;=\;1 + 2\sin\theta \end{Bmatrix}$

A) Once around clockwise, starting at (2,1)

$\displaystyle \begin{Bmatrix}x \;=\;2\cos\theta \\ y \;=\;1 + 2\sin\theta \end{Bmatrix}\quad 0 \,\le \theta \,\le\,2\pi$

B) Three times around counterclockwise, starting at (2,1)

$\displaystyle \begin{Bmatrix}x \;=\;2\cos\theta \\ y \;=\;1 + 2\sin\theta \end{Bmatrix}\quad 0 \,\le\,\theta\,\le\,6\pi$

C) halfway around counterclockwise, starting at (3,0)

Is there a typo?
The point (3,0) is not on the circle.

4. ## Re: parametric equations

can you explain how you got those equations please? i dont understand...

5. ## Re: parametric equations

can you show your work like you did before please? im not following...

6. ## Re: parametric equations

and for C.) the point should be (0,3)

7. ## Re: parametric equations

Originally Posted by pnfuller
can you explain how you got those equations please? i dont understand...
Surely you know that \displaystyle \displaystyle \begin{align*} \left(r\cos{\theta}\right)^2 + \left(r\sin{\theta}\right)^2 = r^2 \end{align*} by the Pythagorean Identity...