with(plots):

x0:=2*cos(t);

y0:=2*sin(t);

x:=x0-cos(2*t);

y:=y0-sin(2*t);

p1:=plot([x,y,t=0..2*Pi],

scaling=constrained,axes=none,

color=blue):

p2:=plot([cos(t),sin(t),t=0..2*Pi],scaling=constrained,axes=none,color=red):

p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=pink,frames=50):

xx:=expand((1-s)*x0+s*x);

yy:=expand((1-s)*y0+s*y);

p4:=animate([xx,yy,s=0..1],t=0..2*Pi,scaling=constrained,axes=none,color=green,thickness=3,frames=50):

n:=3;

with(plots):

x0:=n*cos(t);

y0:=n*sin(t);

x:=x0-cos(n*t);

y:=y0-sin(n*t);

p1:=plot([x,y,t=0..2*Pi],scaling=constrained,axes=none,color=blue):

p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],scaling=constrained,axes=none,color=red):

p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=pink,frames=50):

xx:=expand((1-s)*x0+s*x);

yy:=expand((1-s)*y0+s*y);

p4:=animate([xx,yy,s=0..1],t=0..2*Pi,scaling=constrained,axes=none,color=gray,thickness=3,frames=50):

n:=-2;

with(plots):

x0:=n*cos(t);

y0:=n*sin(t);

x:=x0-cos(n*t);

y:=y0-sin(n*t);

p1:=plot([x,y,t=0..2*Pi],scaling=constrained,axes=none,color=blue):

p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],scaling=constrained,axes=none,color=red):

p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=pink,frames=50):

xx:=expand((1-s)*x0+s*x);

yy:=expand((1-s)*y0+s*y);

p4:=animate([xx,yy,s=0..1],t=0..2*Pi,scaling=constrained,axes=none,color=gray,thickness=3,frames=50):

n:=-3;

with(plots):

x0:=n*cos(t);

y0:=n*sin(t);

x:=x0-cos(n*t);

y:=y0-sin(n*t);

p1:=plot([x,y,t=0..2*Pi],scaling=constrained,axes=none,color=blue):

p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],scaling=constrained,axes=none,color=red):

p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=pink,frames=50):

xx:=expand((1-s)*x0+s*x);

yy:=expand((1-s)*y0+s*y);

p4:=animate([xx,yy,s=0..1],t=0..2*Pi,scaling=constrained,axes=none,color=gray,thickness=3,frames=50):

n:=-2;

with(plots):

x0:=n*cos(t);

y0:=n*sin(t);

x1:=-cos(n*t);

y1:=-sin(n*t);

x:=x0+x1;

y:=y0+y1;

p1:=plot([x,y,t=0..2*Pi],scaling=constrained,axes=none,color=blue):

p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],scaling=constrained,axes=none,color=red):

p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=pink,frames=50):

xx:=expand((1-s)*x0+s*x);

yy:=expand((1-s)*y0+s*y);

p4:=animate([xx,yy,s=0..1],t=0..2*Pi,scaling=constrained,axes=none,color=pink,thickness=3,frames=50):

q3:=animate([x1+n*cos(s),y1+n*sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=gray,frames=50):

xxx:=expand((1-s)*x1+s*x);

yyy:=expand((1-s)*y1+s*y);

q4:=animate([xxx,yyy,s=0..1],t=0..2*Pi,scaling=constrained,axes=none,color=gray,thickness=3,frames=50):

n:=-3;

with(plots):

x0:=n*cos(t);

y0:=n*sin(t);

x1:=-cos(n*t);

y1:=-sin(n*t);

x:=x0+x1;

y:=y0+y1;

p1:=plot([x,y,t=0..2*Pi],scaling=constrained,axes=none,color=blue):

p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],scaling=constrained,axes=none,color=red):

p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=pink,frames=50):

xx:=expand((1-s)*x0+s*x);

yy:=expand((1-s)*y0+s*y);

p4:=animate([xx,yy,s=0..1],t=0..2*Pi,scaling=constrained,axes=none,color=pink,thickness=3,frames=50):

q3:=animate([x1+n*cos(s),y1+n*sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=gray,frames=50):

xxx:=expand((1-s)*x1+s*x);

yyy:=expand((1-s)*y1+s*y);

q4:=animate([xxx,yyy,s=0..1],t=0..2*Pi,scaling=constrained,axes=none,color=gray,thickness=3,frames=50):

n:=3;

with(plots):

x0:=n*cos(t);

y0:=n*sin(t);

x1:=-cos(n*t);

y1:=-sin(n*t);

x:=x0+x1;

y:=y0+y1;

p1:=plot([x,y,t=0..2*Pi],scaling=constrained,axes=none,color=blue):

p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],scaling=constrained,axes=none,color=red):

p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=pink,frames=50):

xx:=expand((1-s)*x0+s*x);

yy:=expand((1-s)*y0+s*y);

p4:=animate([xx,yy,s=0..1],t=0..2*Pi,scaling=constrained,axes=none,color=pink,thickness=3,frames=50):

q3:=animate([x1+n*cos(s),y1+n*sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=gray,frames=50):

xxx:=expand((1-s)*x1+s*x);

yyy:=expand((1-s)*y1+s*y);

q4:=animate([xxx,yyy,s=0..1],t=0..2*Pi,scaling=constrained,axes=none,color=gray,thickness=3,frames=50):

n:=2;

with(plots):

x0:=n*cos(t);

y0:=n*sin(t);

x1:=-cos(n*t);

y1:=-sin(n*t);

x:=x0+x1;

y:=y0+y1;

p1:=plot([x,y,t=0..2*Pi],scaling=constrained,axes=none,color=blue):

p2:=plot([(n-1)*cos(t),(n-1)*sin(t),t=0..2*Pi],scaling=constrained,axes=none,color=red):

p3:=animate([x0+cos(s),y0+sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=pink,frames=50):

xx:=expand((1-s)*x0+s*x);

yy:=expand((1-s)*y0+s*y);

p4:=animate([xx,yy,s=0..1],t=0..2*Pi,scaling=constrained,axes=none,color=pink,thickness=3,frames=50):

q3:=animate([x1+n*cos(s),y1+n*sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,axes=none,color=gray,frames=50):

xxx:=expand((1-s)*x1+s*x);

yyy:=expand((1-s)*y1+s*y);

q4:=animate([xxx,yyy,s=0..1],t=0..2*Pi,scaling=constrained,axes=none,color=gray,thickness=3,frames=50):