Any explicit and implicit relation between

*and*

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

**theta**Thus the equations

**r=f(theta)**or,

*determine curves ,*

**F=(r, theta)=0**The co-ordinates of two points symmetrically situated about the initial line are of the form

*and*

**(r, theta)**

**(r, -theta)**So, that their vertical angles differ in sign only .

Hence a curve will be symmetrical about the initial line if ,

on changing

*to*

**theta**

**-theta .**its equation does not change. For instance the curve

**r=a(1+cos theta)**is symmetrical about the initial line , for ;

**r=a(1+cos theta)=a[1+cos(-theta)]**It may be noted that ;

*represents a circle with its center at the pole and radius*

**r=a**

**a***represents the line through the pole obtained by revolving the initial line through the angle*

**theta=b**

**b**.