Optimizing the proximity.

Calculus Level 3

A helicopter is flying along the curve given by \(y=x^{2}+7\). A soldier placed at \((3,7)\) wants to shoot down the helicopter. He would find it feasible to do so when It is closest to him. Find this closest distance. If your answer is \(a\) , enter the value of \(a^{2}\) in the answer box.

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