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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
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The correct answer is:
$x+y=6$
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 $\frac{x}{6}+\frac{y}{6}=1 \Rightarrow x+y=6$
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 $\frac{x}{6}+\frac{y}{6}=1 \Rightarrow x+y=6$
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