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

• A

  $3 x+y=9$
• B

  $5 x+7 y=35$
• Correct answer
  C

  $x+y=6$
• D

  $5 x+y=10$

Solution

Given $a+b=12$
Now, Area of triangle (A) $=\frac{1}{2} a b$ $\Rightarrow A=\frac{1}{2} a(12-a)$ Since, $\frac{d A}{d a}=\frac{12-2 a}{2}=b-a$ for $\max$ of $A, \frac{d A}{d a}=0 \Rightarrow a=b$ So $b=12-6=6$ So equation of line $\frac{x}{6}+\frac{y}{6}=1 \Rightarrow x+y=6$

Hence, the correct answer is option: 'C'.