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  4. A man starts walking from the point P (-3,4), touches the x-axis at R, and then turns to reach at the point Q (0,2). The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then 50(( PR )2+( RQ )2) is equal to

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Q. A man starts walking from the point $P (-3,4)$, touches the $x$-axis at $R$, and then turns to reach at the point $Q (0,2)$. The man is walking at a constant speed. If the man reaches the point $Q$ in the minimum time, then $50\left(( PR )^{2}+( RQ )^{2}\right)$ is equal to ____

JEE MainJEE Main 2021Application of Derivatives

Solution:

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$50\left( PR ^{2}+ RQ ^{2}\right)$
$50(20+5)$
$50(25)$
$=1250$