Chapter 10.1, Problem 63ES

Consider the family of curves described by the parametric equations $x=a\cos t+h,y=b\sin t+k\left(0\le t\le 2\pi \right)$ where $a\ne 0\text{ and }b\ne 0.$ Describe the curves in this family if

(a) h and k are fixed but a and b can vary

(b) a and b are fixed but h and k can vary

(c) $a=1\text{ and }b=1,$ but h and k vary so that $h=k+1.$