parametric equations

**pnfuller** · August 30th 2012, 07:44 AM

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)

please help!!!!!

**Prove It** · August 30th 2012, 09:43 AM

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)

please help!!!!!

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

**Soroban** · August 30th 2012, 10:23 AM

Hello, pnfuller!

Find parametric equations for the path of particle that moves along $x^2 + (y-1)^2 \:=\:4$ in the manner described.

The equation represents a circle with center $(0,1)$ and radius $r =2.$

Code:

                |
              * * *
          *     |     *
        *       |       *
       *        |        *
                |
      *         |         *
      *        1* - - - - o(2,1)
      *         |         *
                |
  -----*--------+--------*-----
        *       |       *
          *     |     *
              * * *
                |

The parametric equations are: . $\begin{Bmatrix}x \;=\;2\cos\theta \\ y \;=\;1 + 2\sin\theta \end{Bmatrix}$

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

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

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

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

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

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

**pnfuller** · August 30th 2012, 12:37 PM

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

**pnfuller** · August 30th 2012, 04:20 PM

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

**pnfuller** · August 30th 2012, 04:22 PM

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

**Prove It** · August 30th 2012, 07:32 PM

Originally Posted by pnfuller

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

Surely you know that $\displaystyle \begin{align*} \left(r\cos{\theta}\right)^2 + \left(r\sin{\theta}\right)^2 = r^2 \end{align*}$ by the Pythagorean Identity...

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