Finding the radius of a Circle Touching a Parabola and the Axis

Hi Forum!

I have a little problem with a question:

What is the radius of a a circle that touches the parabola 1/2x² at (2,2) and the x-axis?

Here the derivative of our parabola is y=x

And if we get

This could give us the common point between those two circles; that would be the center of the circle that we want.

But this gives me a strange equation, that I really don't know what it is for.

Or,

Get the center (a,b)

and use it at the circle equation.

But where does (2,2) enters here?

I saw something about using both at the same equation, like:

Is this possible? Aren't x and y fixed values here?

Thanks! I can't find a good source to research on this.