Any explicit or implicit relation between

*and*

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

**theta**Thus the equations ;

*or*

**r=f(theta)**

**F(r , theta)=0**determine curves .

The co-ordinates of two points symmetrically situated about the initial line are of the form

*and*

**(r,Theta)***so that their vertical angles differ in sign only .*

**(r,-theta)**Hence a curve will be symmetrical about the initial line if on changing

*to*

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

**-theta**

**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 pole and radius*

**r=a***; and*

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

**theta=b***.*

**b**A few important curves will not be traced . To trace polar curves , we generally consider the variations in

*as*

**r***varies .*

**theta**
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