Find the locus of a particle which moves in the first quadrant so that it is equidistant from the lines x = 0 and y = 0 (where k is a constant)?

  • A x + y = 0
  • B x - y = 0
  • C x + y + k = 0
  • D x - y - k = 0
jamb 2009mathematics

The correct answer is B. x - y = 0

The locus of points that are equidistant from two given lines is the bisector of the angle between those lines. In this case, the given lines are x = 0 and y = 0, which are the x-axis and y-axis, respectively.

The angle between the x-axis and y-axis is 90 degrees. The bisector of this angle would be the line that passes through the origin at a 45-degree angle, which corresponds to a line with a slope of 1.

The equation of a line with slope 1 passing through the origin (0,0) is y = x

So, the correct answer is x - y = 0.

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