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WBJEE · Maths · Straight Lines

A moving line intersects the lines \(x+y=0\) and \(x-y=0\) at the points A, B respectively such that the area of the triangle with vertices \((0,0), A \& B\) has a constant area \(C\). The locus of the mid-point \(A B\) is given by the equation

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

Answer & Solution

Correct Answer

(B) \(\left(x^{2}-y^{2}\right)^{2}=C^{2}\)

Step-by-step Solution

Detailed explanation

Let mid point of \(\mathrm{AB}=(\mathrm{h}, \mathrm{k})\) Let, \(A=(\alpha,-\alpha), B=(\beta, \beta)\) \(\therefore \beta+\alpha=2 \mathrm{~h}, \quad \beta-\alpha=2 \mathrm{k}\) Area…