Circles - Common Polar Coordinate Graphs

Let us come across at the equations of circles in polar coordinates.

1. r = a .

This equation is saying that there is no matter what angle we have got the distance from the origin have to be a.  If you think about it that is precisely the definition of a circle of radius a centered at the origin.

Thus, this is a circle of radius a centered at the origin. This is as well one of the reasons why we might wish to work in polar coordinates. Equation of a circle centered at the source has a very nice equation, not like the corresponding equation in Cartesian coordinates.

2. r = 2a cos θ

We looked at a particular instance of one of these when we were converting equations to Cartesian coordinates.

This is a circle of radius |a| and center (a,0) . 

Note: a might be negative (as it was in our instance above) and thus the absolute value bars are needed on the radius. Though they should not be utilized on the center.

3. r = 2b sin θ

This is identical to the previous one.  It is a circle of radius |b| and center (0, b).

4. r = 2a cos θ + 2b sin θ.

This is a combination of the preceding two and by completing the square two time it can be displayed that this is a circle of radius √(a² + b²) and center (a, b).  In another words, this is the common equation of a circle that is not centered at the origin.