if a,b,c are in ap a,x,b are in gp and b,y,c are in gp the point ( x,y) lies on

a,b,c are in AP then
b= (a+c)/2
a,x,b are in GP then
x^2= ab
b,y,c are in GP then
y^2= bc
x^2+y^2= b(a+c)
now, since a+c = 2b
x^2+y^2= 2b^2
so the point (x,y) lies on a circle with centre (0,0) and radius v2b