Intersection of Focal Chords of an Ellipse

Question

This is the original Question. My Question is more of like a starting point for this question. And believe me this is not a homework question.

Let $\mathbb{E}$ be an ellipse with focii $S$ and $S'$. Let $AB$ and $CD$ be 2 focal chords of the ellipse (Both pass through $S$). Let $AC$ and $BD$ intersect at $K$. Prove that $K$ lies on the directrix corresponding to focus $S$.