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 from the soldier at point \( Q(3, 7) \) to the helicopter flying along the curve \( y = x^2 + 7 \), we can follow these steps:

### Step 1: Define the distance function
Let the point on the curve be \( P(x, y) \), where \( y = x^2 + 7 \). The distance \( D \) between points \( P(x, x^2 + 7) \) and \( Q(3, 7) \) can be expressed as:
\[ D = \sqrt{(x - 3)^2 + (y - 7)^2} \]
Substituting \( y = x^2 + 7 \):
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