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MHT CET202611 April 2026Evening ShiftMathematicsApplication of DerivativesActual

The tangent to the curve y^2 - xy + 9 = 0 is vertical when

Options

  1. Ay = 0
  2. By = 3
  3. Cy = 1 2
  4. Dy = 3

Correct answer

D. y = 3

Step-by-step solution

Given the equation of the curve: y^2 - xy + 9 = 0 Differentiating both sides with respect to x , we get: 2y dy dx - ( y + x dy dx ) = 0 dy dx (2y - x) = y dy dx = y 2y - x For the tangent to be vertical, its slope dy dx must approach infinity. This occurs when the denominator is zero and the numerator is non-zero: 2y - x = 0 x = 2y Substituting x = 2y into the equation of the curve: y^2 - (2y)y + 9 = 0 y^2 - 2y^2 + 9 = 0 -y^2 + 9 = 0 y^2 = 9 y = 3 For y = 3 , the numerator y 0 , so the tangent is indeed vertical.

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