# Circle Tangent to a Parabola?

Geometry Level 5

The above picture shows the graphs of the parabola $$y = x^{2}$$ and the line $$y = -\frac{1}{2}x$$ in Cartesian coordinates. A circle with center $$(p, 0)$$, where $$p > 0$$, is tangent to both the parabola and the line. What is the value of $$p$$ rounded to three decimal places?

Graph generated in Desmos.

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