Conic Sections and Parametric Equations · Superchallenge problem

For any point $P$ on the hyperbola $\dfrac{x^2}{4}-\dfrac{y^2}{12}=1$, let $d_1$ and $d_2$ be the distances from $P$ to the two asymptotes. The product $d_1d_2$ is the same for every $P$. Find it.