COMEDK · Maths · 10. Straight Lines
A variable line \(\frac{x}{a}+\frac{y}{b}=1\) is such that \(a+b=4\). The locus of the mid-point of the portion of the line intercepted between the axes is
- A \(x+y=4\)
- B \(x+y=8\)
- C \(x+y=1\)
- D \(x+y=2\)
Answer & Solution
Correct Answer
(D) \(x+y=2\)
Step-by-step Solution
Detailed explanation
We have, equation of line \(\frac{x}{a}+\frac{y}{b}=1\). Let \(P(h, k)\) be the required point. Now, coordinates \(A\) and \(B\) are \((a, 0)\) and \((0, b)\) respectively. Since, \(P\) is mid-point of \(A B\). Therefore, \((h, k)=\left(\frac{a+0}{2}, \frac{0+b}{2}\right)\)…
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