7-10

> restart;

> x:=t*cos(t):

> y:=t*sin(t):

> a:=plot([x,y,t=0..6*Pi],color=red,scaling=constrained):

> a:;

> x1:=diff(x,t):

> y1:=diff(y,t):

> x2:=diff(x1,t):

> y2:=diff(y1,t):

> f:=x1^2+y1^2:

> g:=x1*y2-y1*x2:

> r:=f^(3/2)/abs(g):

> xc:=x-f/g*y1:

> yc:=y+f/g*x1:

> b:=plot([xc,yc,t=0..6*Pi],color=blue,scaling=constrained):

> b:

> with(plots):

> c:=animate([xc+r*cos(s),yc+r*sin(s),s=0..2*Pi],t=0..6*Pi,color=green,scaling=constrained,frames=30):

> c:

> display(a,c):;

> d:=animate([(1-s)*xc+s*x,(1-s)*yc+s*y,s=0..1],t=0..6*Pi,color=brown,scaling=constrained,frames=30,title="press button here"):

> d:

> display(a,c,d,axes=none);

>

>