$$\frac{x^2}{4}+\frac{y^2}{49}=1$$

Algebra Level 2

If real numbers $$x$$ and $$y$$ satisfy $\frac{x^2}{4}+\frac{y^2}{49}=1,$ the maximum value of $$x+y$$ is $$\sqrt{k}.$$ What is $$k?$$

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