Determine the parametric equations of the path of a particle that travels the ci

Question

Determine the parametric equations of the path of a particle that travels the circle. Please also explain how you did it.

Determine the parametric equations of the path of a particle that travels the circle: (x-2)2y 1)2 36 time interval of osis2 if the particle makes one full circle starting at the point (8, 1) traveling counterclockwise x( t ) = 2+6*cos(t) y( t ) = 1+6*sin(t) on a time interval of 0 S 2T: You are correct. Previous Tries Your receipt no. is 154-2257/ if the particle makes one full circle starting at the point (2,7) traveling clockwise x( t ) = 6"cos(t)+1 y( t ) = 6.sin(t)+2 Submit Answer Incorrect. Tries 4/8 Previous Tries if the particle makes one half of a circle starting at the point (8,1) traveling clockwise x(t)= y(t)- Submit Answer Tries 0/8

Explanation / Answer

Consider the general case (x - h)² + (y - k)² = r². Divide both sides by r²:
[(x - h)/r]² + [(y - k)/r]² = 1
And we know that
[cos(t)]² + [sin(t)]² = 1
To make this so, set cos(t) = (x - h)/r and sin(t) = (y - k)/r and solve for x and y:
x = h + r cos(t)
y = k + r sin(t)
Looking at your circle, we see that h = 2, k = 1, and r = 6, so parametric equations that trace the circle are
(a) x = 2 + 6 cos(t)
y = 1+ 6 sin(t)                       0 ? t ? 2?

(b)A point (2,7)

x=2+6sin(t)

y=1+6cos(t)

(c) at the point (8,1)     0 ? t ? ?

x=2-6cos(t)

y=1+6sin(t)

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