Symmetric Matrices & Quadratic Forms · Easy problem

The symmetric matrix $A = \begin{pmatrix}2 & 2\\2 & 5\end{pmatrix}$ has eigenvalues $6$ and $1$, and $\begin{pmatrix}1\\2\end{pmatrix}$ is an eigenvector for $6$. An eigenvector for $1$ has the form $\begin{pmatrix}a\\1\end{pmatrix}$. Find $a$.