COMEDK · Maths · 10. Straight Lines
If a straight line passing through a fixed point \((a, b)\), where \(a, b > 0\), makes positive intercepts OA and OB on the coordinate axes, then the least value of OA + OB is:
- A \(\left(\sqrt{a} + \sqrt{b}\right)^2\)
- B \(a + b\)
- C \(\left(\sqrt{a} + \sqrt{b}\right)^3\)
- D \(\left(\sqrt{a} - \sqrt{b}\right)^2\)
Answer & Solution
Correct Answer
(A) \(\left(\sqrt{a} + \sqrt{b}\right)^2\)
Step-by-step Solution
Detailed explanation
Let the intercepts on the coordinate axes be \(\alpha\) and \(\beta\). The equation of the line is \(\dfrac{x}{\alpha} + \dfrac{y}{\beta} = 1\). Since the line passes through \((a, b)\), we have \(\dfrac{a}{\alpha} + \dfrac{b}{\beta} = 1\). We need to find the minimum value of…
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