Let $T_x$ and $T_y$ be two random variables that desribe the remaining lifetimes of two persons, aged $x$ and $y$ respectively. The joint density of $T_x$ and $T_y$ is given by
$$f(s,t)=\begin{cases}C(50^2-(s-t)^2),& s,t \in [0,50]\\0, &\mathrm{otherwise}\end{cases}$$
($T_x$ and $T_y$ are not independent). $C>0$ is a normalizing constant.
How can I determine $C$?