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>    restart;

>    with(plots):

>    x:=cos(3*t);y:=sin(4*t);

x := cos(3*t)

y := sin(4*t)

>    x1:=diff(x,t); y1:=diff(y,t);

x1 := -3*sin(3*t)

y1 := 4*cos(4*t)

>    x2:=diff(x1,t); y2:=diff(y1,t);

x2 := -9*cos(3*t)

y2 := -16*sin(4*t)

>    w:=x1*y2-y1*x2; v:=x1^2+y1^2;

w := 48*sin(3*t)*sin(4*t)+36*cos(4*t)*cos(3*t)

v := 9*sin(3*t)^2+16*cos(4*t)^2

>    r:=v^(3/2)/abs(w);

r := (9*sin(3*t)^2+16*cos(4*t)^2)^(3/2)/abs(48*sin(3*t)*sin(4*t)+36*cos(4*t)*cos(3*t))

>    xc:=x-v/w*y1; yc:=y+v/w*x1;

xc := cos(3*t)-4*(9*sin(3*t)^2+16*cos(4*t)^2)/(48*sin(3*t)*sin(4*t)+36*cos(4*t)*cos(3*t))*cos(4*t)

yc := sin(4*t)-3*(9*sin(3*t)^2+16*cos(4*t)^2)/(48*sin(3*t)*sin(4*t)+36*cos(4*t)*cos(3*t))*sin(3*t)

>    p1:=plot([x,y,t=0..2*Pi],scaling=constrained,color=green):

>    p2:=animate([xc+r*cos(s),yc+r*sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,color=red,frames=100):

>    p3:=animate([(1-s)*xc+s*x,(1-s)*yc+s*y,s=0..1],t=0..2*Pi,scaling=constrained,color=blue,frames=100):

>    display(p1,p2,p3,thickness=3,axes=none,view=[-3..3,-3..3]);

[Maple Plot]

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