### Tracing of Curves in Polar Co-ordinates

1) If

*be replaced by*

**theta***and the equation remains unaltered, the curve is symmetrical about the initial line .*

**-theta**2) If only even powers of

*occur in the equation, the curve is symmetrical about the pole or origin .*

**r**3) The curve is symmetrical about the line

**theta=pi/2**If the equation remains unaltered when

*is changed into*

**theta***or when*

**pi-theta***is changed into*

**theta**

**-theta**and

*into*

**r**

**-r.**d) The curve is symmetrical about the line

**theta=pi/4**if the equation of the curves remains unaltered when

*is changed into*

**theta**

**(pi/2)-theta**------ If the curve passes through the pole, The value of

*for which*

**theta***is*

**r***gives the tangent at the pole.*

**zero**------ In most popular equations only periodic functions occur and so

value of

*from*

**theta***to*

**0**

**2pi**need alone be consider.

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