### Spiral

**Spirals are of three kinds :-****1) Equiangular Spiral or Logarithmic Spiral :-**

Its equation is

**r=ae to the power (theta cot alfa)**As

*ranges from*

**theta**

**-infinity to infinity.***ranges from*

**r**

**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.

Thus;

**r=ut**and

**theta= omega.t**Hence;

**a=u/omega****3) Reciprocal Spiral.**

**r=a/theta.**Clearly,

**y=r.sine theta**

**=(r.sine theta.theta)/theta**

**=(a.sine theta)/theta**therefore;

**y=Lt theta-->0 (a.sine theta)/theta=a**therefore;

*is any asymptote .*

**y=a**
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