A student Sumit is running on a playground along the curve given by \(y = x^2 + 7\). Another student Amit standing at a point with co-ordinates (3,7) on the playground wants to hit Sumit by paper ball, when Sumit is nearest to him.
Based on the above information answer the following.
Distance between Sumit and Amit in terms of \(x\) is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\sqrt{(x - 3)^2 + x^4}\)
Sumit is at \(P(x, x^2 + 7)\) and Amit at A(3, 7). By the distance formula,
\( \displaystyle PA = \sqrt{(x - 3)^2 + (x^2 + 7 - 7)^2} \)
\( \displaystyle = \sqrt{(x - 3)^2 + x^4} \)
Option (2) is the square of this distance, not the distance.