Thread: 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)

please help!!!!!

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.

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.

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

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

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

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...