# The 2 Tangent Parabolas

Calculus Level 3

On a vertical parabola $$P_1$$, pick a point $$T$$. Another vertical parabola $$P_2$$ is tangent to $$P_1$$ at $$T$$. Spanning through all possible parabolas $$P_2$$, what is the locus of the focus of $$P_2$$?

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