Two particles P and Q located at the points P t , t 3 - 16 t - 3 , Q t + 1 , t 3 - 6 t - 6 are moving in a plane, the minimum distance between the points in their motion is

Question

Two particles P and Q located at the points P t , t 3 - 16 t - 3 , Q t + 1 , t 3 - 6 t - 6 are moving in a plane, the minimum distance between the points in their motion is, 1, 5, 169, 49

MARKS App · Accepted Answer

P t , t 3 - 16 t - 3 , Q t + 1 , t 3 - 6 t - 6 ⇒ P Q = ( t + 1 - t ) 2 + t 3 - 6 t - 6 - t 3 + 16 t + 3 2 = 1 + ( 10 t - 3 ) 2 Let, y = P Q 2 = 1 + 10 t - 3 2 Minimum value of y will be at d y d t = 0 i.e. 2 10 t - 3 = 0 or t = 3 10 ∴ minimum distance = 1 + 10 × 3 10 - 3 2 = 1

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