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MHT CET202613 April 2026Morning ShiftMathematicsApplication of DerivativesActual

The equation of the normal to the curve xy + 7 = 0 is Ax + By + C = 0 , then

Options

  1. AA > 0, B > 0 or A < 0, B < 0
  2. BA > 0, B < 0
  3. CA 0
  4. DC = 0

Correct answer

A. A > 0, B > 0 or A < 0, B < 0

Step-by-step solution

The given equation of the curve is xy + 7 = 0 . Differentiating with respect to x , we get: x dy dx + y = 0 dy dx = - y x Substituting y = - 7 x , we get: dy dx = 7 x^2 Since x^2 > 0 for all x 0 , the slope of the tangent dy dx > 0 . The slope of the normal is given by - dx dy = - x^2 7 The given equation of the normal is Ax + By + C = 0 , which has a slope of - A B . Equating the slopes, we have: - A B 0 This implies that A and B must have the same sign. Therefore, either A > 0, B > 0 or A Answer: A > 0, B > 0 or

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