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AP EAMCET202315 May 2023Evening ShiftMathematicsApplication of DerivativesActual

If a line is moving between the coordinate axes such that the sum of the intercepts made by it on the coordinate axes is always 12 , then the equation of that line which forms a triangle of maximum area with the coordinate axes is

Options

  1. A3 x+y=9
  2. B5 x+7 y=35
  3. Cx+y=6
  4. D5 x+y=10

Correct answer

C. x+y=6

Step-by-step solution

Given a+b=12 Now, Area of triangle (A) = 1 2 a b A= 1 2 a(12-a) Since, d A d a = 12-2 a 2 =b-a for of A, d A d a =0 a=b So b=12-6=6 So equation of line x 6 + y 6 =1 x+y=6

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