restart;
kappa:=simplify((df*ddg-ddf*dg)/(df^2+dg^2)^(3/2));
f:=cos(t)*(2+sin(5*t));
g:=sin(t)*(2+sin(5*t));
df:=diff(f,t);
dg:=diff(g,t);
ddf:=diff(df,t);
ddg:=diff(dg,t);
t0:=0;
kappa0:=simplify(subs(t=t0,kappa));
evalf(kappa0);
rho:=1/kappa0;
nx:=simplify(subs(t=t0,-dg/sqrt(df^2+dg^2)));
ny:=simplify(subs(t=t0,df/sqrt(df^2+dg^2)));
x0:=subs(t=t0,f)+rho*nx;
y0:=subs(t=t0,g)+rho*ny;
eq:=(x-x0)^2+(y-y0)^2=rho^2;
h:=lhs(eq)-rhs(eq);
with(plots):
P1:=contourplot(h,x=-2..4,y=-1..7,contours=[0],
    grid=[200,200],scaling=constrained):
P2:=plot([f,g,t=0..2*Pi],scaling=constrained):
display(P1,P2);