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MHT CET20244 May 2024Morning ShiftMathematicsApplication of DerivativesActual

The sum of intercepts on coordinate axes made by tangent to the curve x + y = a is

Options

  1. Aa
  2. B2 a
  3. C2 a
  4. D2 a

Correct answer

A. a

Step-by-step solution

x + y = a Differentiating w.r.t. x , we get 1 2 x + 1 2 y ~d y ~d x =0 Slope of the tangent is d y ~d x =- y x Equation of the tangent at (x₁, y₁ ) is (y-y₁ )=- y₁ x₁ (x-x₁ ) aligned & x₁ y+ y₁ x= x₁ y₁+ y₁ x₁ & y₁ x+ x₁ y= x₁ y₁ ( x₁ + y₁ ) & y₁ x+ x₁ y= x₁ y₁ a & x x₁ a + y y₁ a =1 & x -intercept +y -intercept = a ( x₁ + y₁ ) & = a a = a aligned

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