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MHT CET202410 May 2024Evening ShiftMathematicsApplication of DerivativesActual

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

Options

  1. A-2,7
  2. B7,-2
  3. C2,-7
  4. D-7,-2

Correct answer

C. 2,-7

Step-by-step solution

y^2= p x^3+ q ...(i) Differentiating both sides w.r.t. x , we get aligned & 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 aligned 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 . 9=2 8+q q=-7

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