Beside the Cartesian , there are other systems also for representing points and curve analytically . Polar system which is one of them .

---------In this system we started with a fixed line

**OX**called the Initial Line and a fixed point on it , called the Pole .

---------If

**P**be any given point, the distance

**OP=r**is called the Radius Vector and Angle

**XOP=theta**the Vectorial Angle . The two together are referred to as the Polar Co-ordinates of

**P**.

**Unrestricted Variation of Polar Co-ordinates :-**If we concerned with assigning polar co-ordinates to only individual points in the plane , then it would clearly be enough to consider the radius vector to have positive values only and the vectorial angle

**theta**to lie between

**0 and 2pi**.

**Transformation of Co-ordinates :-**Take the initial line

**OX**of the polar system as the positive direction of

**X-axis**and the Pole

**O**as origin for the Cartesian system .The positive direction of

**Y-axis**is to be such that the line

**OX**after revolving through

**Half Pi**is counter - clockwise direction comes to consider with it .

**Polar Equation of Curves :-**Any explicit and implicit relation between

**r**and theta will give a curve determined by the points whose co-ordinates satisfy that relation .

--------- Thus the Equations .

**r=f(theta)**or

**F(r,theta)**

determines Curves .