7-11

> restart;

> x:=3*cos(t)+cos(-3*t):;

> y:=3*sin(t)-sin(-3*t):;

> a:=plot([x,y,t=-Pi..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..2*Pi],color=blue,scaling=constrained):

> b:;

> 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,color=green,scaling=constrained,frames=30):

> c:;

> d:=animate([(1-s)*xc+s*x,(1-s)*yc+s*y,s=0..1],t=0..2*Pi,color=brown,scaling=constrained,frames=30,title="press here",thickness=2):

> d:;

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

>