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Let the shortest distance between the point (2,5)(2,5)(2,5) and the parabola y=x2y=x^2y=x2 be
12⋅a−4bb,\frac 12 \cdot \sqrt{a-4b\sqrt{b}},21⋅a−4bb,
where aaa and bbb are coprime. Find a+b.a+b.a+b.
Bonus: Generalize this for the point (h,h2+1).\big(h,h^2+1\big).(h,h2+1).
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