Graph each plane curve defined by the parametric equations for t in [0, 2π] Then find a rectangular equation for the plane curve. See Example 3.


x = 2 cos t , y = 2 sin t

In Exercises 9–20, use point plotting to graph the plane curve described by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. x = 2t, y = |t − 1|; −∞ < t < ∞

In Exercises 21–40, eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. (If an interval for t is not specified, assume that −∞ < t < ∞. x = t, y = 2t

In Exercises 57–58, the parametric equations of four plane curves are given. Graph each plane curve and determine how they differ from each other. x = t and y = t² − 4

For each plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. See Examples 1 and 2.

x = t + 2 , y = t ―4 , for t in (― ∞ , ∞)

Graph each plane curve defined by the parametric equations for t in [0, 2π] Then find a rectangular equation for the plane curve. See Example 3.

x = 4 sin t , y = 3 cos t

Graph each plane curve defined by the parametric equations for t in [0, 2π] Then find a rectangular equation for the plane curve. See Example 3.

x = 2 + sin t , y = 1 + cos t

Graph each plane curve defined by the parametric equations for t in [0, 2π] Then find a rectangular equation for the plane curve. See Example 3.

x = 1 + cos t , y = sin t ― 1

Which of the following best describes the graph of the parametric equations $x=t^2+2t$ and $y=-t$ as $t$ varies over all real numbers?