Parabola and point

Calculus Level 4

Let the shortest distance between the point (2,5)(2,5) and the parabola y=x2y=x^2 be

12a4bb,\frac 12 \cdot \sqrt{a-4b\sqrt{b}},

where aa and bb are coprime. Find a+b.a+b.


Bonus: Generalize this for the point (h,h2+1).\big(h,h^2+1\big).

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