Parametric Equations
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 \(a+b\)?