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AP EAMCET201921 Apr 2019Evening ShiftMathematicsApplication of DerivativesActual

If 2 y = 3 x - 1 is a tangent drawn to the curve y 2 = a x 3 + b at ( 1 , 1 ) where a , b are constants, then ( a , b ) =

Options

  1. A( 1 , 0 )
  2. B( 0 , 1 )
  3. C( 1 , - 1 )
  4. D( - 1 , 1 )

Correct answer

A. ( 1 , 0 )

Step-by-step solution

It is given that 2   y = 3   x - 1 is tangent to y 2 = a x 3 + b at a point ( 1 , 1 ) with slope 3 2 Differentiate the above equation w.r.t. x , 2 y d y d x = 3 a x 2 d y d x = 3 ax 2 2 y At ( 1 , 1 ) d y d x = 3 a ( 1 ) 2 2 ( 1 ) = 3 a 2 The slope is, d y d x = 3 2 3 a 2 = 3 2 a = 1 The point ( 1 , 1 ) lies on y 2 = a x 3 + b 1 2 = 1 × 1 3 + b b = 0 The point is ( 1 , 0 ) .

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