Spirals are of three kinds :-
1) Equiangular Spiral or Logarithmic Spiral :-
Its equation is r=ae to the power (theta cot alfa)
As theta ranges from -infinity to infinity.
r ranges from theta to infinity.
The curve has a characteristic property that the tangent makes a constant angle with the radius vector
i.e. phay=alfa (constant)
origin is not on the curve.
2) Spiral or Archimedes :-
The equation is r=a theta
This is a curve described by a point which moves along a straight line with constant velocity while the line rotates with constant angular velocity about a fixed point in it.
and theta= omega.t
3) Reciprocal Spiral.
Clearly, y=r.sine theta
therefore; y=Lt theta-->0 (a.sine theta)/theta=a
therefore; y=a is any asymptote .