I think the better Idea would be to first apply basic scaling transformation on your circle to make its origin at (0,0) so that calculations become easier and so the points that you mentioned would become points as (5,0) and (0,-5). i.e. ( +2 in x value and -3 in y value ) for shifting origin and points. Finally, there will be two curves C1 and C2. C1 for that curve that goes forward and C2 for that line that comes back.
Now for curve part we might want to use poolar coordinates.
(x,y) = (5cos(t),5sin(t)); for center at origin.
now reversing transformation for curve part yields:
Curve C1: (x,y) = (5cos(t) -2 ,5sin(t) + 3)
where t goes from 3π/2 to 2π. This give anticlockwise curve.
And for reverse line part. is simple line equation as :
Curve C2: y-3 = x-3 ; as x,y goes from 3 to -2.
I Tried to put it in desmos.
Desmos Link: https://www.desmos.com/calculator/gjrtzitvmo
Picture From Desmos
Only Curve Image for clarity
Disclaimer: This answer is not by an expert. Seniors are requested to rectify if any mistake is done here. Thanks.