Question

WHAT IS MEANT BY LOCUS OF A LINE

Answer 1

   Locus y = f(x) or  f(x,y) = c of a point (x,y) is the path taken by the point (x,y) when  a certain condition or constraint is followed.  Locus can also be taken as the set of all points that satisfy the given constraint.

  Locus of a point (x,y) such that its distance from a fixed point (say origin) is constant is a circle, as  in  x² + y² = r².

  In three dimensions,  it is a sphere,  x²+y²+z² = r²

      All the points on the locus satisfy this constraint, that the distance from origin  is r.

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Locus  in three dimensions of line in 2-dimension is the curved surface that is generated or traced, when given conditions are followed.

Suppose there is a line x = a   in 2-dimensions.  This line is rotated around y axis in the x-z plane.  Then the locus of the line (all points on the line), is a cylindrical surface with central axis as the y axis.  the locus will be
 
             x² + z² = a²,  for any y from -infinity to +infinity.