examday

/TMUA

For every choice of $a<0<b$, let $P=(a,a^2)$ and $Q=(b,b^2)$. The tangents to $y=x^2$ at $P$ and $Q$ meet at $R$, and $C_{a,b}$ is the circle through $P,Q,R$.

A point $X=(u,v)$ must lie strictly inside every circle $C_{a,b}$.

What is the greatest possible value of $u^2$?