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AP EAMCET201726 Apr 2017Morning ShiftMathematicsApplication of DerivativesActual

An angle between the curves x^2=3 y and x^2+y^2=4 is

Options

  1. A⁻¹ 5 3
  2. B⁻¹ 5 3
  3. C⁻¹ 2 3
  4. D3

Correct answer

A. ⁻¹ 5 3

Step-by-step solution

Given curves are On solving Eqs. (i) and (ii), we get x= 3 , y=1 Thus, their points of intersection are ( 3 , 1) and (- 3 , 1) . Now, from Eq. (i), d y d x = 2 x 3 and from Eq. (ii), d y d x =- x y To calculate angle, any of the point can be taken so we are taking ( 3 , 1) as the point of intersection. Now, let m₁ and m₂ be the slope of tangent to the curves at ( 3 , 1) . Then, m₁= 2 3 3 and m₂=- 3 Now, the angle between two curves aligned & = | m₁-m₂ 1+m₁ m₂ |= | 2 3 3 -(- 3 ) 1+ 2 3 3 (- 3 ) | & = | ( 5 3 3 ) (-1

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