The tangency point

Geometry Level 5

Let there be 2 graphs of 2 parabolas, \((1): y = x^2\), \((2): x=y^2\) as shown in the figure.

The graph of the parabola \((1) \) moves along the \(y\)-axis from the bottom to the top as the parabola \((2) \) shifts to the right.

What is the sum of coordinates of the tangency of the point?

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