Multiple choice

The number of circles which passes through the origin and cut off equal chords of $\sqrt { 2 } $ units from the straight lines $y=x$ and $y=-x$, is

  1. $2$
  2. $3$
  3. $4$
  4. $5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A circle passing through the origin has the form x^2 + y^2 + 2gx + 2fy = 0. The distance from the center (-g, -f) to the lines x-y=0 and x+y=0 must be such that the chord length is sqrt(2). Solving this yields 4 possible circles.

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