The parametric equations are and and .
Rewrite the equation.
The sum of there squares are equal
Trigonometric identity : .
The above equation is in form of general form of circle.
So the particle moves in circle path.
Draw a table for different values of ranging from .
Determine the direction of the curve.
Graph:
The parametric equations are and
Observe the graph:
From to , thecircle completes it first revolution in clockwise.
Similarly the ellipse completes it second and third revolution at and .
The particle moves counter clockwise around the circle path.
The particle moves counter clockwise around the circle path.
The equation is .
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