Question

represent a circle in polar form with centre as origin

Answer 1

Polar coordinate system  The polar coordinate system is a two-dimensional coordinate system in which each point P on a plane is determined by the length of its position vector r and the angle q between it and the positive direction of the x-axis, where 0 < r < + oo  and  0 < q < 2p.Polar and Cartesian coordinates relations

Since the inverse tangent function (arctan or tan-1) returns values in the range  -p/2 < q < p/2, then

for points lying in the 2nd or 3rd quadrantand for points lying in the 4th quadrant