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The acute angle of intersection of the curves x 2 y = 1 and y = x 2 in the first quadrant is θ , then tan ⁡ θ is equal to

Options

  1. A1
  2. B2 3
  3. C3 4
  4. D4 3

Correct answer

D. 4 3

Step-by-step solution

Solving the equation of the curves, we get 1 x 2 = x 2 ⇒ x = ± 1 ∴ Intersection point is 1,1 in the first quadrant. Now, x 2 y = 1 ⇒ y = 1 x 2 ⇒ d y d x = - 2 x 3 ⇒ m 1 = - 2 (by putting x = 1 ) And y = x 2 ⇒ d y d x = 2 x ⇒ m 2 = 2 ∴ tan ⁡ θ = m 1 - m 2 1 + m 1 m 2 = 4 3

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