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AP EAMCET202123 Aug 2021Morning ShiftMathematicsApplication of DerivativesActual

The sum of the lengths of the subtangent and the subnormal drawn at = 3 on the cycloid x=a( - ) : y=a(1- ) is

Options

  1. A2 a
  2. B(2 3 ) a
  3. C2 a 3
  4. Da 3

Correct answer

C. 2 a 3

Step-by-step solution

Given = / 3 and x=a( - ), y=a(1- ) Differentiate it, w.r.t. ' d x d =a(1- ), d y d =a( ) Then, d y d x = a a(1- ) = 1- ( d y d x )_ = / 3 = / 3 1- / 3 = 3 / 2 1-1 / 2 = 3 Slope of tangent = 3 aligned & Length of subtangent = (y)_ = / 3 m &= a(1- / 3) 3 = a(1 / 2) 3 = a 2 3 aligned Length of subnormal aligned & =(y)_ = / 3 m=a(1- / 3) 3 & =a (1- 1 2 ) 3 = a 3 2 aligned Sum of Eqs. (i) and (ii), aligned a 2 3 + a 3 2 & = 3 a 6 + a 3 2 = 3 a+3 3 a 6 & = 4 3 a 6 = 2 3 a 3 = 2 a 3 aligned Sum of length of subtangent and

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