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MHT CET202526 Apr 2025Morning ShiftMathematicsApplication of DerivativesActual

The equation of the tangent to the curve (1+x^2 ) y=2-x , where it crosses the X-axis, is

Options

  1. Ax+5 y=2
  2. Bx-5 y=2
  3. C5 x-y=10
  4. D5 x+y-10=0

Correct answer

A. x+5 y=2

Step-by-step solution

The curve (1 + x^2)y = 2 - x intersects the X-axis when y = 0 , yielding x = 2 at the point of tangency (2, 0) . Differentiating implicitly using the product rule: 2x y + (1 + x^2) dy dx = -1 . At (2, 0) , this simplifies to 5 dy dx = -1 , so the slope is m = - 1 5 . Using point-slope form: y = - 1 5 (x - 2) , which simplifies to x + 5y = 2 . The correct answer is: A

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