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AP EAMCET20228 Jul 2022Evening ShiftMathematicsApplication of DerivativesActual

If the angle between the curves y^2=4 x and y=e^ -x / 2 is , then cosec ^2( / 2)=

Options

  1. A2
  2. B3
  3. C3
  4. D2

Correct answer

A. 2

Step-by-step solution

The given curves are y^2=4 x and y=e^ -x / 2 . Let (x₁, y₁ ) be the point of intersection of both curves. Now, y^2=4 x array ll & d y d x = 2 y & m₁= ( d y d x )_ (x₁, y₁ ) = 2 y₁ array Also, y=e^ -x / 2 array ll & d y d x = (- 1 2 ) e^ -x / 2 & m₂= ( d y d x )_ (x₁, y₁ ) =- 1 2 e^ -x₁ / 2 =- 1 2 y₁ array Given that is the angle between the curves. = | m₂-m₁ 1+m₁ m₂ |= | - y₁ 2 - 2 y₁ 1+ (- y₁ 2 2 y₁ ) |= = / 2 Now, cosec ^2( / 2)= cosec ^2( / 4)=( 2 )^2=2

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