Bisecting Two Pancakes

Geometry Level 3

Let K1K_1 denote the region of R2\mathbb{R}^2 bounded by the ellipse with equation (x9)29+(y9)216=1,\frac{(x-9)^2}{9} + \frac{(y-9)^2}{16} = 1, and let K2K_2 denote the region bounded by the ellipse with equation (x+1)216+(y+3)29=1.\frac{(x+1)^2}{16} + \frac{(y+3)^2}{9} = 1. There is a unique line \ell which simultaneously bisects K1K_1 and K2K_2 into two pieces of equal area.

What is the yy-intercept of ?\ell?

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