x2 + y2 = a2

Substitute the polar conversions into this equation

(rcosq)2 + (rsinq)2 = a2

r2cos2q + r2sin2q = a2
r2(cos2q + sin2q) = a2
r2 = a2
r = a

Where cos2q + sin2q = 1,
the Pythagorean Identity