Bisecting Two Pancakes

Geometry Level 3

Let $K_1$ denote the region of $\mathbb{R}^2$ bounded by the ellipse with equation $\frac{(x-9)^2}{9} + \frac{(y-9)^2}{16} = 1,$ and let $K_2$ denote the region bounded by the ellipse with equation $\frac{(x+1)^2}{16} + \frac{(y+3)^2}{9} = 1.$ There is a unique line $\ell$ which simultaneously bisects $K_1$ and $K_2$ into two pieces of equal area.

What is the $y$ -intercept of $\ell?$