# Ellipse, ellipse and ellipse :P

Geometry Level 4

Consider the ellipse $$\frac{x^2}{f(k^2+2k+5)}+\frac{y^2}{f(k+11)}=1$$, where $$f(x)$$ is a positive decreasing function, then the value of $$k$$ for which major axis coincides with the $$x-axis$$ can be expressed in the form of $$k \in (a,b)$$. Find $$a+b$$

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