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MHT CET202314 May 2023Evening ShiftMathematicsApplication of DerivativesActual

If y=4 x-5 is a tangent to the curve y^2= p x^3+ q at (2,3) , then p - q is

Options

  1. A-5
  2. B5
  3. C9
  4. D-9

Correct answer

C. 9

Step-by-step solution

y^2= p x^3+ q ... (i) Differentiating both sides w.r.t. x , we get gathered 2 y d y ~d x =3 p x^2 d y ~d x = 3 p 2 ( x^2 y ) ( d y ~d x )_ (2,3) = 3 p 2 4 3 =2 p gathered Slope of the line y=4 x-5 is 4 . Since the line touches the curve, their slopes are equal. 2 p =4 p =2 Since (2,3) lies on y^2= p x^3+ q . array ll & 9=2 8+q q=-7 & p-q=2+7=9 array

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