> restart:

> x:=evalf(t+sin(t)):

> y:=evalf(cos(t)):

> a:=plot([x,y,t=-Pi..5*Pi],color=brown,scaling=constrained,axes=none):

> x1:=diff(x,t):

> y1:=diff(y,t):

> x2:=diff(x1,t):

> y2:=diff(y1,t):

> r:=(x1^2+y1^2)^(3/2)/abs(x1*y2-x2*y1):

> xc:=x-(x1^2+y1^2)*y1/(x1*y2-x2*y1):

> yc:=y+(x1^2+y1^2)*x1/(x1*y2-x2*y1):

> b:=plot([xc,yc,t=-Pi..5*Pi],color=blue,scaling=constrained,axes=none):

> with(plots):

Warning, the name changecoords has been redefined

> c:=animate([xc+r*cos(s),yc+r*sin(s),s=0..2*Pi],t=-Pi..5*Pi,frames=50,color=green,scaling=constrained,axes=none):

>

> d:=animate([(1-s)*xc+s*x,(1-s)*yc+s*y,s=0..1],t=-Pi..5*Pi,frames=50,color=red,scaling=constrained,axes=none):

> display(a,b,c,d);

> restart:

> x:=evalf(5*cos(t)):

> y:=evalf(3*sin(t)):

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

> x1:=diff(x,t):

> y1:=diff(y,t):

> x2:=diff(x1,t):

> y2:=diff(y1,t):

> r:=(x1^2+y1^2)^(3/2)/abs(x1*y2-x2*y1):

> xc:=x-(x1^2+y1^2)*y1/(x1*y2-x2*y1):

> yc:=y+(x1^2+y1^2)*x1/(x1*y2-x2*y1):

> b:=plot([xc,yc,t=0..2*Pi],color=blue,scaling=constrained,axes=none):

> with(plots):

Warning, the name changecoords has been redefined

> c:=animate([xc+r*cos(s),yc+r*sin(s),s=0..2*Pi],t=0..2*Pi,frames=50,color=green,scaling=constrained,axes=none):

>

> d:=animate([(1-s)*xc+s*x,(1-s)*yc+s*y,s=0..1],t=0..2*Pi,frames=50,color=red,scaling=constrained,axes=none):

> display(a,b,c,d);

> restart:

> x:=evalf(5*cos(t)-cos(2*t)):

> y:=evalf(3*sin(t)-sin(2*t)):

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

> x1:=diff(x,t):

> y1:=diff(y,t):

> x2:=diff(x1,t):

> y2:=diff(y1,t):

> r:=(x1^2+y1^2)^(3/2)/abs(x1*y2-x2*y1):

> xc:=x-(x1^2+y1^2)*y1/(x1*y2-x2*y1):

> yc:=y+(x1^2+y1^2)*x1/(x1*y2-x2*y1):

> b:=plot([xc,yc,t=0..2*Pi],color=blue,scaling=constrained,axes=none):

> with(plots):

Warning, the name changecoords has been redefined

> c:=animate([xc+r*cos(s),yc+r*sin(s),s=0..2*Pi],t=0..2*Pi,frames=50,color=green,scaling=constrained,axes=none):

>

> d:=animate([(1-s)*xc+s*x,(1-s)*yc+s*y,s=0..1],t=0..2*Pi,frames=50,color=red,scaling=constrained,axes=none):

> display(a,b,c,d);

> restart:

> x:=evalf(cos(t)/(2-cos(t)^2)):

> y:=evalf(sin(t)*cos(t)/(2-cos(t)^2)):

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

> x1:=diff(x,t):

> y1:=diff(y,t):

> x2:=diff(x1,t):

> y2:=diff(y1,t):

> r:=(x1^2+y1^2)^(3/2)/abs(x1*y2-x2*y1):

> xc:=x-(x1^2+y1^2)*y1/(x1*y2-x2*y1):

> yc:=y+(x1^2+y1^2)*x1/(x1*y2-x2*y1):

> b:=plot([xc,yc,t=0..2*Pi],color=blue,scaling=constrained,axes=none):

> with(plots):

Warning, the name changecoords has been redefined

> c:=animate([xc+r*cos(s),yc+r*sin(s),s=0..2*Pi],t=0..2*Pi,frames=50,color=green,scaling=constrained,axes=none):

>

> d:=animate([(1-s)*xc+s*x,(1-s)*yc+s*y,s=0..1],t=0..2*Pi,frames=50,color=red,scaling=constrained,axes=none):

> display(a,c,d,view=[-2..2,-2..2]);

> restart:

> x:=evalf(5*cos(t)+sin(2*t)):

> y:=evalf(3*cos(3*t)-sin(4*t)):

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

> x1:=diff(x,t):

> y1:=diff(y,t):

> x2:=diff(x1,t):

> y2:=diff(y1,t):

> r:=(x1^2+y1^2)^(3/2)/abs(x1*y2-x2*y1):

> xc:=x-(x1^2+y1^2)*y1/(x1*y2-x2*y1):

> yc:=y+(x1^2+y1^2)*x1/(x1*y2-x2*y1):

> b:=plot([xc,yc,t=0..2*Pi],color=blue,scaling=constrained,axes=none):

> with(plots):

> c:=animate([xc+r*cos(s),yc+r*sin(s),s=0..2*Pi],t=0..2*Pi,frames=50,color=green,scaling=constrained,axes=none):

>

> d:=animate([(1-s)*xc+s*x,(1-s)*yc+s*y,s=0..1],t=0..2*Pi,frames=50,color=red,scaling=constrained,axes=none):

> display(a,c,d,view=[-10..10,-10..10]);

> restart:

> x:=evalf(t*cos(t)):

> y:=evalf(t*sin(t)):

> a:=plot([x,y,t=0..8*Pi],color=brown,scaling=constrained,axes=none):

> x1:=diff(x,t):

> y1:=diff(y,t):

> x2:=diff(x1,t):

> y2:=diff(y1,t):

> r:=(x1^2+y1^2)^(3/2)/abs(x1*y2-x2*y1):

> xc:=x-(x1^2+y1^2)*y1/(x1*y2-x2*y1):

> yc:=y+(x1^2+y1^2)*x1/(x1*y2-x2*y1):

> b:=plot([xc,yc,t=0..2*Pi],color=blue,scaling=constrained,axes=none):

> with(plots):

> c:=animate([xc+r*cos(s),yc+r*sin(s),s=0..8*Pi],t=0..8*Pi,frames=50,color=green,scaling=constrained,axes=none):

>

> d:=animate([(1-s)*xc+s*x,(1-s)*yc+s*y,s=0..1],t=0..8*Pi,frames=50,color=red,scaling=constrained,axes=none):

> display(a,c,d);

>