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MHT CET202522 Apr 2025Evening ShiftMathematicsApplication of DerivativesActual

The normal to the curve x=9(1+ ), y =9 at always passes through the fixed point

Options

  1. A(9,0)
  2. B(8,9)
  3. C(0,9)
  4. D(9,8)

Correct answer

A. (9,0)

Step-by-step solution

Fixed point analysis for the normal to the parametric curve The parametric curve is defined by x = 9(1 + ) and y = 9 . The slope of the tangent is dy dx = - , so the slope of the normal is . The equation of the normal becomes y - 9 = (x - 9(1 + )) . Multiplying through by and simplifying yields: (x - 9) - y = 0 . For this equation to hold for all , the coefficients of and must vanish: x - 9 = 0 and y = 0 . Thus, the fixed point is (9, 0) , corresponding to option A.

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