I can find the fractions:
-0.333... → -1/3;  0.8333... → 5/6;  1.138888... → 41/36
  [ see here ]
(x + 1/3)² + (y − 5/6)² = 41/36
[or:   3·x² + 3·y² + 2·x − 5·y − 1 = 0]

We can draw the circle with (possiamo tracciare il cerchio con) circle_2  (see the code;  se also here).

Let's check with  (Controlliamo con)  R:

source("http://macosa.dima.unige.it/r.R")
x=c(3,0,3,2,-5,-1)
Conic(x)
# C1=function(x,y)  3 * x^2 + 0 * x*y + 3 * y^2 + 2 * x + -5 * y + -1 
# circle  xC = -0.3333333  yC = 0.8333333  R = 1.067187 
PLANE(-2,1,-1,2)
CURVE(C1,"red")
POINT(-1/3,0.833333,"blue")
fraction(R^2)
# 41/36
#       Or:
F = function(x,y) 3*x^2 + 3*y^2 + 2*x - 5*y - 1
PLANE(-2,1,-1,2)
CURVE(F,"brown")
POINT(-1/3,0.833333,"blue")

With Desmos:


or:   

If the circle is a "point" and if it does not exist ("NaN" stands for "Not a Number"):