If the p coordinate is (x, y) and the f coordinate is (x, 0) (according to the tangent of the circle to the X axis).

PF=PB

(x-x)^2+(y-0)^2=(x-0)^2+(y-3)^2

y^2=x^2+y^2-6y+9

y=(x^2+9)/6

A circle is not necessarily tangent to the y axis.

Has nothing to do with the y=x line.

When x=y=3, the circle p is tangent to the y axis.