                   Defining Equations for various Curves.
                   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1) Cardoid.  [OCGen_1]
            Polar Co-ordinates:-
                  r = 2a(1 - kCosT)      [T = Theta]; True Cardoid when k = 1

2) Limacon.  [OCGen_2]
            Polar Co-ordinates:-
                  r = 2aCosT + k      When k = 2a Curve is Cardioid
                                      When k = a Curve is Trisectrix

3) Astroid.  [OCGen_8]
            Cartesian Co-ordinates:-
                  x = aCos^3t
                  y = aSin^3t        or x(Exp2/3) + y(Exp2/3) = a(Exp2/3)

4) Nephroid.  [OCGen_9]
            Cartesian Co-ordinates:-
                  x = 3aCost + aCos3t
                  y = 3aSint + aSin3t

5) Deltoid.  [OCGen_7]
            Cartesian Co-ordinates:-
                  x = aCost + 2aCos(0.5t)
                  y = aSint - 2aSin(0.5t)

6) Equiangular Spiral. [OCGen_3]
             Polar Co-ordinates:-
                  r = Rk^t         t = angle

7) Lemniscate of Bernoulli. [OCGen_4]
             Polar Co-ordinates:-
                  r^2 = a^2Cos2T       [T = Theta]

8) Catenary. [OCGen_10]
             Cartesian Co-ordinates:-
                  y = cCosh(x/c)

9) Cissoid of Deocles. [OCGen_5]
             Polar Co-ordinates:-
                  r = 2a(SecT - CosT)       [T = Theta]

10) Parallel Spiral. [OCGen_6]
             Polar Co-ordinates:-
                  (r - a)^2 = b^2T          [T = Theta]

                   
                  