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AP EAMCET202124 Aug 2021Evening ShiftMathematicsApplication of DerivativesActual

If the relation p (subnormal length) =q (subtangent length) ^2 holds true for the curve b y^2=(x+a)^3 , then the value of p q is equal to

Options

  1. A8 27
  2. B8 b 27
  3. C8 27 b
  4. D27 8 b

Correct answer

B. 8 b 27

Step-by-step solution

Given curve, b y^2=(x+a)^3 On differentiating w.r.t. x , we get 2 b y d y d x =3(x+a)^2 aligned & Length of subnormal =y d y d x =y ( 3(x+a)^2 2 b y ) & Length of subtanget =y d x d y =y ( 2 b y 3(x+a)^2 ) aligned Given, P( Subnormal length )=q( subtangent length) ^2 P (y d y d x )=q (y d x d y )^2 P q =y ( d x d y )^3 P q =y ( 2 b y 3(x+a)^2 )^3= 8 y^4 27 b^3 ((x+a)^3 ]^2 P q = 8 b 27 ( b y^2 (x+a)^3 )^2 P q = 8 b 27 [ b y^2=(x+a)^3 ]

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