Any explicit or implicit relation between r and theta will give a curve determined by the points whose co-ordinates satisfies that relation .
Thus the equations ;
r=f(theta) or F(r , theta)=0
determine curves .
The co-ordinates of two points symmetrically situated about the initial line are of the form (r,Theta) and (r,-theta) so that their vertical angles differ in sign only .
Hence a curve will be symmetrical about the initial line if on changing theta to -theta its equation does not change . For instance the curve
is symmetrical about the initial line , for
It may be noted that
r=a represents a circle with its center at pole and radius a ; and
theta=b represents a line through the pole obtained by revolving the initial line through the angle b .
A few important curves will not be traced . To trace polar curves , we generally consider the variations in r as theta varies .