Parabola and point

Calculus

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

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

where $a$ and $b$ are coprime. Find $a+b.$

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