> a:=2:b:=1:c:=1.2:d:=b*sqrt(1-c^2/a^2):e:=sqrt(a^2-b^2):
f1:=t->(c+e)*cos(t)+d*sin(t): f2:=t->-e*cos(t)+sqrt(a^2*cos(t)^2+b^2*sin(t)^2):
f:=f1+f2:
C1:=[f(t),t,t=0..2*Pi]:
d:=d+1:
f1:=t->(c+e)*cos(t)+d*sin(t): f2:=t->-e*cos(t)+sqrt(a^2*cos(t)^2+b^2*sin(t)^2):
f:=f1+f2:
C2:=[f(t),t,t=0..2*Pi]:
d:=d-1.8:
f1:=t->(c+e)*cos(t)+d*sin(t): f2:=t->-e*cos(t)+sqrt(a^2*cos(t)^2+b^2*sin(t)^2):
f:=f1+f2:
C3:=[f(t),t,t=0..2*Pi]:
polarplot([C1,C2,C3],scaling=constrained,axes=none,color=[red,blue,green]);

[Maple Plot]

programme général cissoidale deux cercles

> a:=2:b:=1:c:=1.2:d:=1.9:e:=sqrt(a^2-b^2):aa:=-2*max((c+e+d),e+sqrt(a^2+b^2)):bb:=-aa:
cc:=aa:dd:=-aa:
f1:=t->(c+e)*cos(t)+d*sin(t): f2:=t->-e*cos(t)+sqrt(a^2*cos(t)^2+b^2*sin(t)^2):
f:=f1+f2:
C1:=[f(t),t,t=0..2*Pi]:
C2:=[1/f(t),t,t=0..2*Pi]:
C3:=[1,t,t=0..2*Pi]:
base1:=polarplot([C1],color=red):
base2:=polarplot([[f1(t),t,t=0..2*Pi],[f2(t),t,t=0..2*Pi],[2*f1(t),t,t=0..2*Pi],[2*f2(t),t,t=0..2*Pi]],color=[blue$4],linestyle=[2$2,1$2]):

>

> n:=30:display([base1,base2,
display(
[seq(
display([plot([[[0,0],[f(tt)*cos(tt),f(tt)*sin(tt)]]$2,[[2*f1(tt)*cos(tt),2*f1(tt)*sin(tt)],[2*f2(tt)*cos(tt),2*f2(tt)*sin(tt)]]$2],style=[line,point,line,point],color=black,symbol=[box,circle,box$2])]),tt=seq(2*k*Pi/n,k=0..n-1))],insequence=true)],axes=none);

inverse de conique

> polarplot([C1,C2,C3],view=[-2..4,-2..4],color=[red,blue,black],axes=none,linestyle=[1$2,2$2]);

podaire de conique

> with(linalg):
pi:=evalf(Pi):
x:=t->c+a*cos(t):
y:=t->d+b*sin(t):
x1:=D(x):y1:=D(y):n:=sqrt(x1^2+y1^2):
u:=[x1(t)/n(t),y1(t)/n(t)]:
M:=[x(t),y(t)]:
H:=M-dotprod(M(t),u)*u:
n:=30:
L:=seq(plot([[0,0],H,M],color=black),t=seq(k*2*pi/n,k=0..n-1)):
display([display(L,insequence=true),plot([[x,y,0..2*Pi]],color=blue),base1],axes=none);

-

> a:=2:b:=1:c:=1.2:d:=b*sqrt(1-c^2/a^2):e:=sqrt(a^2-b^2):aa:=-2*max((c+e+d),e+sqrt(a^2+b^2)):bb:=-aa:
cc:=aa:dd:=-aa:
f1:=t->(c+e)*cos(t)+d*sin(t): f2:=t->-e*cos(t)+sqrt(a^2*cos(t)^2+b^2*sin(t)^2):
f:=f1+f2:
C1:=[f(t),t,t=0..2*Pi]:
C2:=[1/f(t),t,t=0..2*Pi]:
C3:=[1,t,t=0..2*Pi]:
base1:=polarplot([C1],color=red):
base2:=polarplot([[f1(t),t,t=0..2*Pi],[f2(t),t,t=0..2*Pi],[2*f1(t),t,t=0..2*Pi],[2*f2(t),t,t=0..2*Pi]],color=[blue$4],linestyle=[2$2,1$2]):
cc:=aa:dd:=-aa:
f1:=t->(c+e)*cos(t)+d*sin(t): f2:=t->-e*cos(t)+sqrt(a^2*cos(t)^2+b^2*sin(t)^2):
f:=f1+f2:
C1:=[f(t),t,t=0..2*Pi]:
C2:=[1/f(t),t,t=0..2*Pi]:
C3:=[1,t,t=0..2*Pi]:
base1:=polarplot([C1],color=red):
base2:=polarplot([[f1(t),t,t=0..2*Pi],[f2(t),t,t=0..2*Pi],[2*f1(t),t,t=0..2*Pi],[2*f2(t),t,t=0..2*Pi]],color=[blue$4],linestyle=[2$2,1$2]):

> n:=30:display([base1,base2,
display(
[seq(
display([plot([[[0,0],[f(tt)*cos(tt),f(tt)*sin(tt)]]$2,[[2*f1(tt)*cos(tt),2*f1(tt)*sin(tt)],[2*f2(tt)*cos(tt),2*f2(tt)*sin(tt)]]$2],style=[line,point,line,point],color=black,symbol=[box,circle,box$2])]),tt=seq(2*k*Pi/n,k=0..n-1))],insequence=true)],axes=none);

inverse de conique

> polarplot([C1,C2,C3],view=[-2..4,-2..4],color=[red,blue,black],axes=none,linestyle=[1$2,2$2]);

podaire de conique

> with(linalg):
pi:=evalf(Pi):
x:=t->c+a*cos(t):
y:=t->d+b*sin(t):
x1:=D(x):y1:=D(y):n:=sqrt(x1^2+y1^2):
u:=[x1(t)/n(t),y1(t)/n(t)]:
M:=[x(t),y(t)]:
H:=M-dotprod(M(t),u)*u:
n:=30:
L:=seq(plot([[0,0],H,M],color=black),t=seq(k*2*pi/n,k=0..n-1)):
display([display(L,insequence=true),plot([[x,y,0..2*Pi]],color=blue),base1],axes=none);

programme général cissoidale deux cercles

> a:=2:b:=1:c:=1.2:d:=b*sqrt(1-c^2/a^2)-0.5:e:=sqrt(a^2-b^2):aa:=-2*max((c+e+d),e+sqrt(a^2+b^2)):bb:=-aa:
cc:=aa:dd:=-aa:
f1:=t->(c+e)*cos(t)+d*sin(t): f2:=t->-e*cos(t)+sqrt(a^2*cos(t)^2+b^2*sin(t)^2):
f:=f1+f2:
C1:=[f(t),t,t=0..2*Pi]:
C2:=[1/f(t),t,t=0..2*Pi]:
C3:=[1,t,t=0..2*Pi]:
base1:=polarplot([C1],color=red):
base2:=polarplot([[f1(t),t,t=0..2*Pi],[f2(t),t,t=0..2*Pi],[2*f1(t),t,t=0..2*Pi],[2*f2(t),t,t=0..2*Pi]],color=[blue$4],linestyle=[2$2,1$2]):

>

> n:=30:display([base1,base2,
display(
[seq(
display([plot([[[0,0],[f(tt)*cos(tt),f(tt)*sin(tt)]]$2,[[2*f1(tt)*cos(tt),2*f1(tt)*sin(tt)],[2*f2(tt)*cos(tt),2*f2(tt)*sin(tt)]]$2],style=[line,point,line,point],color=black,symbol=[box,circle,box$2])]),tt=seq(2*k*Pi/n,k=0..n-1))],insequence=true)],axes=none);

inverse de conique

> polarplot([C1,C2,C3,[0.03,t,t=0..2*Pi]],view=[-2..4,-2..4],color=[red,blue,black],axes=none,linestyle=[1$2,2,1]);

podaire de conique

> with(linalg):
pi:=evalf(Pi):
x:=t->c+a*cos(t):
y:=t->d+b*sin(t):
x1:=D(x):y1:=D(y):n:=sqrt(x1^2+y1^2):
u:=[x1(t)/n(t),y1(t)/n(t)]:
M:=[x(t),y(t)]:
H:=M-dotprod(M(t),u)*u:
n:=30:
L:=seq(plot([[0,0],H,M],color=black),t=seq(k*2*pi/n,k=0..n-1)):
display([display(L,insequence=true),plot([[x,y,0..2*Pi]],color=blue),base1],axes=none);

>

programme général cissoidale deux cercles

> a:=2:b:=1:c:=1.2:d:=1.9:e:=sqrt(a^2+b^2):
f1:=t->(c+e)*cos(t)+d*sin(t): f2:=t->-e*cos(t)+sqrt(a^2*cos(t)^2-b^2*sin(t)^2):
f:=f1+f2:
C1:=[f(t),t,t=0..2*Pi]:
C2:=[1/f(t),t,t=0..2*Pi]:
C3:=[1,t,t=0..2*Pi]:
base1:=polarplot([C1],color=red):
base2:=polarplot([[f1(t),t,t=0..2*Pi],[f2(t),t,t=0..2*Pi],[2*f1(t),t,t=0..2*Pi],[2*f2(t),t,t=0..2*Pi]],color=[blue$4],linestyle=[2$2,1$2]):

>

> n:=30:display([base1,base2,
display(
[seq(
display([plot([[[0,0],[f(tt)*cos(tt),f(tt)*sin(tt)]]$2,[[2*f1(tt)*cos(tt),2*f1(tt)*sin(tt)],[2*f2(tt)*cos(tt),2*f2(tt)*sin(tt)]]$2],style=[line,point,line,point],color=black,symbol=[box,circle,box$2])]),tt=seq(2*k*Pi/n,k=0..n-1))],insequence=true)],axes=none);

inverse de conique

> polarplot([C1,C2,C3],view=[-2..4,-2..4],color=[red,blue,black],axes=none,linestyle=[1$2,2$2]);

podaire de conique

> with(linalg):
pi:=evalf(Pi):
x:=t->c+a/cos(t):
y:=t->d+b*tan(t):
x1:=D(x):y1:=D(y):n:=sqrt(x1^2+y1^2):
u:=[x1(t)/n(t),y1(t)/n(t)]:
M:=[x(t),y(t)]:
H:=M-dotprod(M(t),u)*u:
n:=30:
L:=seq(plot([[0,0],H,M],color=black),t=seq(k*2*pi/n,k=0..n-1)):
display([display(L,insequence=true),plot([[x,y,0..2*Pi]],color=blue),base1],axes=none);