Tangent Circle in a Graph

Is there any more info given for this question.......like the size or equation for the circle?  I think there are MANY circles that would fit the bill.....do you need an answer in terms of the circle size/equation?

Because of symmetry, the center of the circle will lie  at  (0, k)

Let the equation of the  circle be

x^2 + (y - k)^2 = r^2

x^2 + y^2 - 2ky + k^2 = r^2

Using implicit differentiation, the slope of any tangent line to the circle is given by

2x + 2yy' - 2ky'  = 0

x + yy'  - ky' = 0

y'  ( y - k)  =  -x

y' =     [ x ] / [k - y]

The slope of the tangent line to the parabola at any point =   d/dx (x^2) =     2x

So....equating these slopes, we have that

2x =  x / [ k - y]

2 = 1 / [ k - y]

k - y =    1/2

y = k -1/2      this is the y coordinate of the intersection of the parabola and the circle

So.....the difference in the height of the circle's center and the tangent point(s) is just the difference in their  y values

So

k - (k - 1/2)  =    1/2   unit