AP EAMCET · Maths · Straight Lines
A straight line \(L\) with negative slope passes through the point \((1,1)\) and cuts the positive coordinate axes at the points \(A\) and \(B\). If \(O\) is the origin, then the minimum value of \(O A+O B\) as \(L\) varies, is
- A 1
- B 2
- C 3
- D 4
Answer & Solution
Correct Answer
(D) 4
Step-by-step Solution
Detailed explanation
Equation of line having slope ' \(m\) ' passes through the point \((1,1)\) is So, \(A\left(\frac{m-1}{m}, 0\right)\) and \(B(0,1-m)\) Now, \(\quad O A+O B=\left(1-\frac{1}{m}\right)+(1-m)=2-\left(m+\frac{1}{m}\right)\) \(\because \mathrm{m}\) is negative, so minimum value of…
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