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JEE Main20199 Jan 2019Morning ShiftMathematicsApplication of DerivativesActual

If θ denotes the acute angle between the curves, y = 10 - x 2 and y = 2 + x 2 at a point of their intersection, then tan ⁡ θ is equal to:

Options

  1. A4 9
  2. B8 17
  3. C7 17
  4. D8 15

Correct answer

D. 8 15

Step-by-step solution

Intersection points of given curves are ± 2 , 6 , for 1 s t curve d y d x = - 2 x ∴ m 1 = 4 or - 4 For 2 n d curve, d y d x = 2 x ∴ m 2 = - 4 or 4 ∴ | t a n θ | = 4 - - 4 1 + 4 - 4 or - 4 - 4 1 + - 4 4 = 8 15 (In both cases)

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