Let A, B and C be three points on the parabola y^2=6 x and let the line segment A B meet the line L through C parallel to the x -axis at the point D.…

Let $\displaystyle A, B$ and $\displaystyle C$ be three points on the parabola $\displaystyle y^2=6 x$ and let the line segment $\displaystyle A B$ meet the line $\displaystyle L$ through $\displaystyle C$ parallel to the $\displaystyle x$-axis at the point $\displaystyle D$. Let $\displaystyle M$ and $\displaystyle N$ respectively be the feet of the perpendiculars from $\displaystyle A$ and $\displaystyle B$ on $\displaystyle L$. Then $\displaystyle \left(\frac{A M \cdot B N}{C D}\right)^2$ is equal to $\displaystyle \_\_\_\_$.