Let the equation of a circle with center and radius r be: (x-2/3) 2+y 2 = r 2 ................... (1).

Then, the point where the circle is tangent to the given curve is the point p; So the equations formed by these two curves have a unique solution. y^2=2x……(2)

(1) and (2) are combined into a set of equations, and the middle unknown y is eliminated. After simplification, we get:

(x+ 1/3)^2=r^2- 1/3…………………………(3)

When r 2- 1/3 = 0, the equations have a unique solution x =-1/3; At this time, R=√3/3.