Multiple choice

The equation of the circle which passes through origin and cuts off chords of length 2 on the lines $x = y$ and $x = -y$ is

  1. $\mathrm{x}^{2}+\mathrm{y}^{2}\pm 2\sqrt{2}\mathrm{y}=0,\ \mathrm{x}^{2}+\mathrm{y}^{2}\pm 2\sqrt{2}\mathrm{x}= 0$
  2. $\mathrm{x}^{2}+\mathrm{y}^{2}\pm 3\sqrt{3}\mathrm{x}=0,\ \mathrm{x}^{2}+\mathrm{y}^{2}$ $\pm 3\sqrt{3}\mathrm{y}=0$
  3. $\mathrm{x}^{2}+\mathrm{y}^{2}\pm 4\sqrt{2}\mathrm{x}=0,\ \mathrm{x}^{2}+\mathrm{y}^{2}\pm 4\sqrt{2}\mathrm{y}= 0$
  4. $\mathrm{x}^{2}+\mathrm{y}^{2}\pm 4\sqrt{2}\mathrm{x}=0,\ \mathrm{x}^{2}+\mathrm{y}^{2}\pm 4\sqrt{3}\mathrm{y}= 0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The circle passes through the origin, so its equation is x^2 + y^2 + 2gx + 2fy = 0. The chord length formula for a line ax + by + c = 0 is 2 * sqrt(r^2 - d^2). Setting chord length to 2 for lines x=y and x=-y allows solving for g and f.

Keep practicing — related questions