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MHT CET202522 Apr 2025Morning ShiftMathematicsDifferentiationActual

If x=a ^3 y=a ^3 Then 1+ ( d y ~d x )^2 =

Options

  1. A^2
  2. B^2

Correct answer

2

Step-by-step solution

Given the parametric equations x = a ^3 , y = a ^3 , determine 1 + ( d y d x )^2 . Differentiate both with respect to : d x d = -3a ^2 , d y d = 3a ^2 . Using the parametric derivative formula, d y d x = 3a ^2 -3a ^2 = - = - . Substitute into the expression: 1 + (- )^2 = 1 + ^2 = ^2 . Assuming 0 , ^2 = . Final answer: (choice C).

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