SOLUTION: Determine a polar equation for the circle with a radius of sqrt(5) and a center at (1,pi/2).

First we get the rectangular equation of the circle.

The center is the polar point, which is



That's the point that we get when we 
1. swing counter-clockwise  radians or 90° 
   from the right side of the x-axis, and
2. Go out 1 unit in that direction, which
   turns out to be directly upward.

So that's the same point as the rectangular point (0,1)



So the circle with that center and a radius of  is this
black circle:



which has rectangular equation:

 which becomes

 or






Then to change from rectangular to polar or
vice-versa we draw this:

 

From which we see that 
, , and 

So we replace the x2+y2 by r2 and
the y using  solved for y, 

So the rectangular equation  becomes
the polar equation:



Edwin