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

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 = 2 cos t , y = 2 sin 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 = 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

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?

Which of the following best describes the graph of the parametric equations $x=1-t^2$ and $y=2t$?

Given the parametric equations $x=t\cos \left(t\right)$, $y=t$, $z=t\sin \left(t\right)$ for $t\ge 0$, which of the following best describes the graph of these equations?

Which of the following parametric equations represents a circle of radius $3$ centered at the origin, traced counterclockwise as $t$ increases from $0$ to $2\pi$?