Multiple choice

If OA and OB are equal perpendicular chords of the circles $x^2 + y^2 - 2x + 4y = 0$, then equation of OA and OB are where O is origin.

  1. $3x + y = 0$ and $ 3x - y = 0$
  2. $3x + y = 0$ or $3y - x = 0$
  3. $x + 3y = 0$ and $ y - 3x = 0$
  4. $x + y = 0$ or $x - y = 0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The circle is x^2 + y^2 - 2x + 4y = 0, which is (x-1)^2 + (y+2)^2 = 5. The center is (1, -2). Chords OA and OB are perpendicular and equal, passing through the origin. The lines must be symmetric with respect to the line connecting the origin to the center. Testing option C: x + 3y = 0 and y - 3x = 0 are perpendicular (slopes -1/3 and 3).

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