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KCET2022MathematicsApplication of Derivatives

The coordinates of the point on the x + y =6 at which the tangent is equally inclined to the axes is

Options

  1. A(4,4)
  2. B(1,1)
  3. C(9,9)
  4. D(6,6)

Correct answer

C. (9,9)

Step-by-step solution

Given, x + y =6 x + y =6 Differentiating w.r.t. x , we get 1 2 x + 1 2 y d y d x =0 d y d x =- y x Since, the tangent is equally inclined to the axes. aligned & d y d x = 1 - y x = 1 & y = x y=x & aligned Therefore, x + y =6 x + x =6 2 x =6 aligned & x =3 x=9 & x=9 aligned

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