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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

  1. A \(x-y=\frac{a}{2}\)
  2. B \(x+y=a\)
  3. C \(x^{2}+y^{2}=4 a^{2}\)
  4. D \(x^{2}-y^{2}=2 a^{2}\)
Verified Solution

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 \((h, k)\)…