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COMEDK2015MathematicsParabola

The angle between the curve y²=4 a x and a y=2 x² is

Options

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

Correct answer

B. ⁻¹ 3 5

Step-by-step solution

We have, y²=4 a x ...(i) and a y=2 x² ...(ii) Solving Eqs. (i) and (ii), we get x=a and y=2 a Differentiating Eq. (i) w.r.t. x , we get 2 y d y d x =4 a Now, [ d y d x ]_ (a, 2 a) = 4 a 2(2 a) =1 m₁=1 Now, differentiating Eq. (ii) w.r.t. x , we get gathered a d y d x =4 x [ d y d x ]_ (a, 2 a) = 4 a a =4 m₂=4 gathered Angle between curves is equal to angle between their tangents. aligned & | m₂-m₁ 1+m₁ m₂ | = | 4-1 1+4 (1) | & = 3 5 = ⁻¹ ( 3 5 ) aligned

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