NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice

The minimum possible distance between the points A a , a - 1 and B b , b 2 + b + 1 ∀ a , b ∈ R is D units, then the value of D 2 is

Correct answer

Step-by-step solution

Given points lie on the line y = x - 1 and the parabola y = x 2 + x + 1 Thus, the minimum distance occurs along the common normal ∴ At B ,   d y d x = 1 or 2 x + 1 = 1 ⇒ x = 0 ∴ B is 0 , 1 Hence, the shortest distance is D = 0 - 1 - 1 2 = 2 units

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