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AP EAMCET201822 Apr 2018Evening ShiftMathematicsApplication of DerivativesActual

The acute angle between the tangents drawn at the point of intersection (other than the origin) of the curves x^2=4 y and y^2=4 x is

Options

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

Correct answer

B. ⁻¹ ( 3 5 )

Step-by-step solution

Point of intersection other then origin is (4,4) . Now, slope of fangents to curve (i) at (4,4) is m₁= . d y d x |_ (4,4) = . 2 x 4 |_ (4,4) =2 and slope of tangent to curve (ii) at (4,4) is m₂= . d y d x |_ (4,4) = . 4 2 y |_ (4,4) = 1 2 So, angle ( ) between the tangents is = | m₁-m₂ 1+m₁ m₂ |= | 2- 1 2 1+2 ( 1 2 ) |= 3 / 2 2 = 3 4 So, = ⁻¹ ( 3 4 )= ⁻¹ ( 3 5 )

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