AP EAMCET · Maths · Application of Derivatives
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 \(5 x+7 y=35\)
- C \(x+y=6\)
- D \(5 x+y=10\)
Answer & Solution
Correct Answer
(C) \(x+y=6\)
Step-by-step Solution
Detailed explanation
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…
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