Parametric Equations and And a Parameter Interval for the Motion $x=2 \cos t, y=2 \sin t, \pi \leq t \leq 2 \pi$

Parametric equations and and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph
traced by the particle and the direction of motion.
- $x=2 \cos t, y=2 \sin t, \pi \leq t \leq 2 \pi$

A) $x ^ { 2 } + y ^ { 2 } = 4$ ; Counterclockwise from
$( 2,0 )$ to $( 2,0 )$ , one rotation


B) $x ^ { 2 } + y ^ { 2 } = 4 ;$ Clockwise from $( 2,0 )$ to $( - 2,0 )$

C) $x ^ { 2 } + y ^ { 2 } = 1$ ; Clockwise from $( 1,0 )$ to $( 1,0 )$


D) $x ^ { 2 } + y ^ { 2 } = 4$ ; Counterclockwise from , one rotation $( - 2,0 )$ to $( 2,0 )$