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

Wotzdorfg 2021-08-11 Answered
Find parametric equations for the following curves. Include an interval for the parameter values.
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A circle centered at (-2, -3) with radius 8, generated clockwise
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## Expert Answer

Cristiano Sears
Answered 2021-08-12 Author has 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, $x=-2+8\mathrm{cos}\left(-t\right)=x=-2+8\mathrm{cos}\left(t\right)$
$y=-3+8\mathrm{sin}\left(-t\right)=y=-3-8\mathrm{sin}\left(t\right)$ Thus, the parametric equation a circle centered at (-2,-3) with radius 8 and generated clockwise is, $x=-2+8\mathrm{cos}\left(t\right),0\le t\le 2\pi$
$y=-3-8\mathrm{sin}\left(t\right),0\le t\le 2\pi$
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