An Apache helicopter of enemy is flying along the curve given by `y=x^2+7`. A soldier, placed at (3, 7), wants to shoot down the helicopter when it is nearest to him. Find the nearest distance.

Explanation

To find the nearest distance between the soldier at point \( Q(3, 7) \) and the helicopter flying along the curve \( y = x^2 + 7 \), we can follow these steps:

### Step 1: Define the distance function
The distance \( D \) between the soldier's position \( Q(3, 7) \) and a point \( P(x, y) \) on the curve is given by the distance formula:
\[ D = \sqrt{(x - 3)^2 + (y - 7)^2} \]
Since \( y = x^2 + 7 \), we can substitute \( y \) into the distance formula:
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