WBJEE · Maths · Straight Lines
The line \(A B\) cuts off equal intercepts \(2 a\) from the axes. From any point \(P\) on the line \(A B\) perpendiculars \(P R\) and \(P S\) are drawn on the axes. Locus of mid-point of \(R S\) is
- A \(x-y=\frac{a}{2}\)
- B \(x+y=a\)
- C \(x^{2}+y^{2}=4 a^{2}\)
- D \(x^{2}-y^{2}=2 a^{2}\)
Answer & Solution
Correct Answer
(B) \(x+y=a\)
Step-by-step Solution
Detailed explanation
\(\Rightarrow\) \[ \begin{array}{l} \frac{x}{2 a}+\frac{y}{2 a}=1 \\ x+y=2 a \end{array} \] Let the coordinates of the mid-point of \(\mathrm{RS}\) be \((\mathrm{h}, \mathrm{k})\) So. \(R\) and \(S\) are \((2 h, 0)\) and \((0,2 k)\) Hence, the mid-point of \(R S\) is \((h, k)\)…
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