AHSME 1975 Problem 5

The polynomial $(x+y)^9$ is expanded in decreasing powers of $x$. The second and third terms have equal values when evaluated at $x=p$ and $y=q$, where $p$ and $q$ are positive numbers whose sum is one. What is the value of $p$? $\textbf{(A)}\ 1/5 \textbf{(B)}\ 4/5 \textbf{(C)}\ 1/4 \textbf{(D)}\ 3/4 \textbf{(E)}\ 8/9$