Question

Find parametric equations and a parameter interval for the motion of a particle starting at the point (2, 0) and tracing the top half of the circle$x ^ { 2 } + y ^ { 2 } = 4$four times.

Solutions

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Step 1
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At the beginning of the task, we notice that the given equation is the equation of the circle with the center at the origin and the radius $r=2$.

Since the particle moves on the upper part of the circle, then we will draw only the part of the circle that is above the $x$-axis.

$\small \text{Figure 1. The part of the circle above the x-axis}$

How do we write a circle as a parametric equation?

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