Wotzdorfg

2021-08-11

Find parametric equations for the following curves. Include an interval for the parameter values.

Answers are not unique.

A circle centered at (-2, -3) with radius 8, generated clockwise

Answers are not unique.

A circle centered at (-2, -3) with radius 8, generated clockwise

Cristiano Sears

Skilled2021-08-12Added 96 answers

Given: A circle centered at (-2, -3) with radius 8, generated clockwise.
To find: the parametric equation a circle centered at (-2, -3) with radius 8 and generated clockwise.
Let h and h be the coordinates of the center of the circle then x and y coordinates in the equation will be:
$x=h+r\mathrm{cos}\left(t\right)$

$y=k+r\mathrm{sin}\left(t\right)$

where x and y are the coordinates of any point on the circle, r is the radius and t is the parameter. Therefore, the parametric equations for the circle centered at (h,k)=(-2,-3)with radius, r=8 is$x=-2+8\mathrm{cos}\left(t\right)$

$y=-3+8\mathrm{sin}\left(t\right)$

Here, the circle is generated clockwise, that is, b<0. Therefore,$x=-2+8\mathrm{cos}(-t)=x=-2+8\mathrm{cos}\left(t\right)$

$y=-3+8\mathrm{sin}(-t)=y=-3-8\mathrm{sin}\left(t\right)$
Thus, the parametric equation a circle centered at (-2,-3) with radius 8 and generated clockwise is,
$x=-2+8\mathrm{cos}\left(t\right),0\le t\le 2\pi$

$y=-3-8\mathrm{sin}\left(t\right),0\le t\le 2\pi$

where x and y are the coordinates of any point on the circle, r is the radius and t is the parameter. Therefore, the parametric equations for the circle centered at (h,k)=(-2,-3)with radius, r=8 is

Here, the circle is generated clockwise, that is, b<0. Therefore,

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