On a separate piece of paper, sketch the graph of the parabola $y = x^2 + 9$. On the same graph, plot the point $(0, -5 )$. Note that there are two tangent lines of $y = x^2 + 9$ that pass through the point $(0, -5 )$.

Specifically, the tangent line of the parabola $y = x^2 + 9$ at the point $(a, a^2 + 9)$ passes through the point $(0, -5 )$ where $a > 0$. The other tangent line that passes through the point $(0, -5 )$ occurs at the point $(-a, a^2 + 9)$.

Find the number $a$.

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