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

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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