Parametrizing Circles Consider the parametric equations (a) Graph the parametric

Chapter 6, Problem 6.1.1.228

(choose chapter or problem)

Parametrizing Circles Consider the parametric equations

\(x=a \cos t, \quad y=a \sin t, \quad 0 \leq t \leq 2 \pi\)

(a) Graph the parametric equations for a= 1, 2, 3, 4 in the same square viewing window.

(b) Eliminate the parameter t in the parametric equations to verify that they are all circles. What is the radius?

Now consider the parametric equations

\(x=h+a \cos t, \quad y=k+a \sin t, \quad 0 \leq t \leq 2 \pi .\)

(c) Graph the equations for a=1 using the following pairs of values for h and k:

(d) Eliminate the parameter t in the parametric equations and identify the graph.

(e) Write a parametrization for the circle with center (-1, 4) and radius 3.