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KCET2009MathematicsApplication of Derivatives

The length of the subtangent at t on the curve x = a ( t + t ), y = a (1- t ) is

Options

  1. Aa t
  2. B2 a ( t 2 ) ( t 2 )
  3. C2 a t 2
  4. D2 a ³ ( t 2 ) ( t 2 )

Correct answer

A. a t

Step-by-step solution

Given, x=a(t+ t), y=a(1- t) dx dt = a (1+ t ), dy dt = a ( t ) d y d x = a t a(1+ t) = t 2 aligned Length of subtangent &= y d y / d x &= a(1- t) t 2 &=2 a t 2 t 2 &=a t aligned

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