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AP EAMCET202018 Sep 2020Morning ShiftMathematicsApplication of DerivativesActual

The curve (3 y^2=2 a x^2+6 b ) passes through the point (P(3,-1) ) and the gradient of the curve at (P ) is " -1 ", then the values of (a ) and (b ) are

Options

  1. A(a= 1 2 , b=-1 )
  2. B(a= -1 2 , b=1 )
  3. C(a= 1 2 , b=1 )
  4. D(a= -1 2 , b=-1 )

Correct answer

A. (a= 1 2 , b=-1 )

Step-by-step solution

Equation of given curve is (3 y^2=2 a x^2+6 b )...(i) ( ) Curve (i) passes through point (P(3,-1) ), so (3=18 a+6 b ) ( 6 a+2 b=1 )...(ii) and the ( . d y d x ,(3,-1)=-1 ) (given), so on differentiating the Eq. (i), we get ( aligned 6 y d y d x & =4 a x 6 (-1) (-1) & =4 a(3) a=1 / 2 aligned ) ( b=-1 ) ( )from Eq. (ii) on putting value of ' (a ) ' )

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