What is the standard form in polar equation of circle and cartiode?

cardiod is
r = a + a cos(theta) OR
r = a + a sin(theta)

circle centered at (h,k)
(x-h)^2 + (y-k)^2 = r^2
covert by letting x = rcos(theta) and y = rsin(theta)
(rcosT - h)^2 + (rsinT - k)^2 = r^2
r^2cos^2(T)-2rhcosT + h^2 + r^2sin^2(T)-2rksinT + k^2 = r^2
r^2 [cos^2(T) + sin^2(T) ] - 2rhcosT-2rksinT + h^2 + k^2 = r^2
r^2(1) - 2rhcosT-2rksinT + h^2 + k^2 = r^2
-2r(hcosT + ksinT) = -h^2 - K^2
r = ( h^2 + k^2 ) / [2 (h cosT + k sinT) ]
where center is (h,k)

r = a cos(theta) is a circle with diameter a on x-axis
r = a sin(theta) is a circlee with diameter a on y-axis