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# Describe the motion of a particle with position $(x, y)$ as $t$ varies in a given interval.$x = 2 + \sin t$, $\; y = 1 + 3\cos t$, $\; \pi/2 \leqslant t \leqslant 2\pi$

## The particle starts at $(3,1)$ then moves 3$/ 4$ of the way around clockwise on the path of an ellipse with center at $(2,1),$ ending at $(2,4)$

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### Video Transcript

The problem is describes a motion that a party always position acts. Why, as to worries in even interval So first you were half X minus two square bus line once wass Sawyer over nine. It's cultural one. This is on the lips centered at this point two one so we can scarce the graph as follows. Center to one your point and what he is he going to high over too half Act two. Three. Why is before too one? I don't want Teo to pie. We have actually got to sue. Why are connected to Monty is equal to two high. Actually go to two. Why go to war? So we're half twenty Worries from pi over to to to high the particle goes from the point three one year in this direction. It was a point shoot for

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#### Topics

Parametric Equations

Polar Coordinates

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