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AP EAMCET201824 Apr 2018Morning ShiftMathematicsApplication of DerivativesActual

If is an angle between the curves x^2+4 y=0 and x y=2 , then =

Options

  1. A-1
  2. B1 3
  3. C1 2
  4. D3

Correct answer

D. 3

Step-by-step solution

Point of intersection of the curves aligned x^2+4 y & =0 and x y=2 x^2 & =-4 y and y= 2 x x^2 & = -8 x x^3 & =-8 x=-2 aligned Slope of first curve at x=-2 aligned 2 x+4 d y d x & =0 d y d x =- x 2 m₁ & = ( d y d x )_ x=-2 = -(-2) 2 =1 aligned Slope of the second curve x y=2 aligned y & = 2 x d y d x & = -2 x^2 m₂ & = ( d y d x )_ x=-2 = -2 (-2)^2 = -1 2 aligned If angle between them , then = | m₁-m₂ 1+m₁ m₂ |= | 1- (- 1 2 ) 1+(1) (- 1 2 ) |= | 3 / 2 1 / 2 |=3

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