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MHT CET202523 Apr 2025Evening ShiftMathematicsApplication of DerivativesActual

The combined equation of the tangent and normal to the curve x y=100 at the point (5,20) is ________.

Options

  1. A15 x^2-15 y^2+16 x y=480
  2. B15 x^2+16 x y-198 x+10 y+480-15 y^2=0
  3. C15 x^2-16 x y+19 x-10 y-480+15 y^2=0
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

Combined equation of tangent and normal to the curve xy=100 at point (5,20) The curve xy=100 has derivative dy dx = - y x by implicit differentiation. At point (5,20) , the tangent slope is m_t = - 20 5 = -4 . The tangent equation using point-slope form: y - 20 = -4(x - 5) simplifies to 4x + y - 40 = 0 . The normal slope is the negative reciprocal: m_n = 1 4 , giving the normal equation y - 20 = 1 4 (x - 5) which simplifies to x - 4y + 75 = 0 . The combined equation of tangent and normal is the product of their equ

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