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 \(\ell?\)

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