A.
\[ f(y)=\left\{ \begin{aligned} -\frac{1}{\pi(a+y)}\sqrt{\frac{a}{y}} &,& y < 0 \\ 0 &,& y \geq 0 \end{aligned} \right. \]
B.
\[ f(y)=\left\{ \begin{aligned} -\frac{1}{\pi(a+y)}\sqrt{\frac{a}{2y}} &,& y < 0 \\ 0 &,& y \geq 0 \end{aligned} \right. \]
C.
\[ f(y)=\left\{ \begin{aligned} -\frac{1}{\pi(a+y)}\sqrt{\frac{a}{2y}} &,& y > 0 \\ 0 &,& y \leq 0 \end{aligned} \right. \]