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# Parametric Equations

As a particle moves, its position can often be written in terms of time. Systems like these can be modeled with parametric equations, which cleverly write coordinates in terms of a parameter.

# Parametric Equations - Graphing

Which of the following is the curve defined by the parametric equations $x=4\sin t, \quad y=8\cos t,$ assuming that $$x_1=y_1=4$$ and $$x_2=y_2=8?$$

If $$(a,b)$$ is the center and $$r$$ is the radius of the circle defined by the parametric equations $x=6\cos 6t, \quad y=6\sin 6t, \quad 0 \leq t \leq 2\pi,$ what is the value of $$a+b+r$$?

Which of the following is the curve defined by the parametric equations $x=6\sin t, \quad y=5\sin^2 t ?$

What shape does the following parametric equation describe:

$x = 3 \cos ^2 \theta, y = 6 \sin^2 \theta.$

Consider the ellipse defined by the parametric equations $x=12\cos t, \quad y=4\sin t,$ where $$0 \leq t \leq 2\pi$$. If the length of the major axis is $$a$$ and the length of the minor axis is $$b$$, what is the value of $$a+b$$?

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