2

Provide a parametrization with the given properties:

The curve is circled at point $(a, b)$. It is traced once counterclockwise, starting at the point $(a+r, b)$ with $t \in[0,2π]$

attempt:

$x = a + r cos(t), y = a+rsin(t)$ for $t \in [0, 2\pi]$

is above not right?

Tinler
  • 1,061
  • I believe your second equation should be $y = b + r\sin\left(t\right)$, but otherwise everything else looks fine to me. Also, with your second line starting with "The curve is circled at ...", I assume "circled" is meant to be "centered". – John Omielan Jan 22 '19 at 01:05
  • Yes it is correct if you change a to b in y. – lightxbulb Jan 22 '19 at 01:05

1 Answers1

0

We have a circle of equation:

$$(x-a)^2+(y-b)^2=r^2$$

Setting $x=a+r\cos(t)$ and $y=b+r\sin t$ gives:

$$(r\cos(t))^2+(r\sin(t))^2=r^2$$

$$\to r^2(\cos^2(t)+\sin^2(t))=r^2$$

which holds because $\cos^2(t)+\sin^2(t)=1$

So your mistake was simply you need $y=b+...$ rather than $y=a+...$

Rhys Hughes
  • 12,842