4-11 Construct the circles with center at (cos(t),sin(t)) and and passing through (2cos(t)/3+cos(2t)/3,2sin(t)/3+sin(2t)/3) with t ranging over [0,2Pi].

The answer is different from teacher's answer!

> restart:

> x:=cos(t):

> y:=sin(t):

> r:=((x-(2*cos(t)/3+cos(2*t)/3))^2+(y-(2*sin(t)/3+sin(2*t)/3))^2)^(1/2):

> m:=[x+r*cos(s),y+r*sin(s),s=0..2*Pi]:

> t:=2*Pi*n/100:

> plot([m$n=0..100],color=red,scaling=constrained,axes=none);

>

Another figure:

> restart:

> x:=cos(t):

> y:=sin(t):

> r:=((x-(2*cos(t)/3+cos(2*t)/3))^2+(y-(2*sin(t)/3-sin(2*t)/3))^2)^(1/2):

> m:=[x+r*cos(s),y+r*sin(s),s=0..2*Pi]:

> t:=2*Pi*n/100:

> plot([m$n=0..100],color=red,scaling=constrained,axes=none);

>