The equation of a circle whose center is on the parabola y ^ 2 = 2x and whose quasilinear and X-axis are tangent

The equation of a circle whose center is on the parabola y ^ 2 = 2x and whose quasilinear and X-axis are tangent

Guide line x = - 1 / 2
Center (a, b)
The distance from the center of the circle to the tangent is equal to the radius
So the distance to the guide line is equal to the distance to the x-axis
That is a - (- 1 / 2) = | B|
a+1/2=|b|
a=|b|-1/2
The center of the circle is on the parabola y ^ 2 = 2x
|b|^2=2a
(a+1/2)^2=2a
a^2-a+1/4=0
(a-1/2)^2=0
a=1/2,|b|=1
r^2=|b|^2=1
So (x-1 / 2) ^ 2 + (Y-1) ^ 2 = 1 and (x-1 / 2) ^ 2 + (y + 1) ^ 2 = 1