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The acute angles between the curves y = 2 x 2 - x and y 2 = x at 0,0 and 1,1 are α and β respectively, then

Options

  1. Aα - β = 0
  2. Bα + β = 0
  3. Cα > β
  4. Dα < β

Correct answer

A. α - β = 0

Step-by-step solution

y = 2 x 2 - x &#8658; d y d x = 4 x - 1 Let, m 1 = 4 x - 1 y 2 = x &#8658; 2 y d y d x = 1 Let, m 2 = d y d x = 1 2 y At P 0,0 , &#160; m 1 = - 1 , &#160; m 2 &#8594; not defined Angle &#945; = &#960; 4 At Q 1,1 , &#160; m 1 = 3 , &#160; m 2 = 1 2 &#946; = t a n - 1 3 - 1 2 1 + 3 2 = &#960; 4

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