Consider the set of lines in the plane at a unit distance from origin and intersecting both $X$-axis and $Y$-axis. Let $S$ be the set of mid points of segments of these lines joining their point of intersection with $X$-axis and $Y$-axis. Then $S$ is

• Correct answer
  A

  $\left\{(x, y): \frac{1}{x^2}+\frac{1}{y^2}=4\right\}$.
• B

  $\left\{(x, y): \frac{1}{x^2}-\frac{1}{y^2}=4\right\}$
• C

  $\left\{(x, y): x^2+y^2=4\right\}$.
• D

  $\left\{(x, y): y^2=4 x\right\}$

Hence, the correct answer is option: 'A'.