Question 4
Let $a$ and $b$ be two real numbers satisfying $a\lt b$, and such that for each real number $m$ satisfying $a\lt m\lt b$, the circle $x^2+(y-m)^2=25$ meets the parabola $4y=x^2$ at four distinct points in the Cartesian plane. Let $S$ be the maximum possible value of $b-a$. Find $\lfloor4S\rfloor$.