Algebra

Parametric Equations

Parametric Equations - Graphing

         

Which of the following is the curve defined by the parametric equations x=4sint,y=8cost ?x=4\sin t, \quad y=8\cos t \ ?

If (a,b)(a,b) is the center and rr is the radius of the circle defined by the parametric equations x=6cos6t,y=6sin6t,0t2π,x=6\cos 6t, \quad y=6\sin 6t, \quad 0 \leq t \leq 2\pi, what is the value of a+b+ra+b+r?

Which of the following is the curve defined by the parametric equations x=6sint,y=5sin2t?x=6\sin t, \quad y=5\sin^2 t ?

What shape does the following parametric equation describe:

x=3cos2θ,y=6sin2θ. x = 3 \cos ^2 \theta, y = 6 \sin^2 \theta.

Consider the ellipse defined by the parametric equations x=12cost,y=4sint,x=12\cos t, \quad y=4\sin t, where 0t2π0 \leq t \leq 2\pi. If the length of the major axis is aa and the length of the minor axis is bb, what is the value of a+ba+b?

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