A Product of Area Ratios

Consider the parabola $x^2=4y$. A point $A$ on the parabola lies in the first quadrant, and the tangent line $l$ at $A$ meets the $x$-axis at a point $B$. The line $l'$ through $B$ perpendicular to $l$ meets the parabola at two points $C$ and $D$, with $C$ in the first quadrant, and meets the $y$-axis at a point $K$. Let $O$ be the origin.

1. If the $x$-coordinate of $A$ is $2$, find the equation of the tangent line $l$. 2. Let $S_1$, $S_2$, $S_3$ denote the areas of $\triangle OKD$, $\triangle OKC$, $\triangle AKC$ respectively. Find the minimum value of