☼ Locus  :   If  a point moves according to some given geometrical conditions, then the path traced out by the moving point is called its Locus ( or Curve ).

■ The locus of  a point equidistant from two given points A and B is the perpendicular bisector of  .

■ The locus of  a point makes an isosceles triangle with a constant base  is also the perpendicular bisector of .

■ The locus of  the vertices of  isosceles triangles having a common base is the perpendicular bisector of  the base.

■ If a point moves in such a way that its distance from a given fixed point is always constant, then the locus of  the path is a circle.

■ The locus of  a point makes a right angle triangle with the base  is also a circle with the diameter .

■ If  AB is a fixed line segment, then the locus of  a point  P  such that ∠APB  =  90^o, is a circle with AB as diameter.

■ AB is a fixed line. The locus of  a point  P  so that AB²  =  AP² + BP² is a circle with AB as diameter.

■ The locus of  mid-points of  equal chords of  a circle is the circle concentric with the given circle and radius equal to the distance of  equal chords from the center.

■ The locus of  mid points of  parallel chords of  a circle is the diameter of  the circle perpendicular to the parallel chords.

■ Locus of  the centers of  all circles passing through two given points A and B is the perpendicular bisector of  AB.

■ If  l  and  m  be two lines such that  l || m. If a point moves in such a way that it is equidistant from  l  and  m, then locus is a line in just mid way between  l  and  m and parallel to each one of  them.

■ The locus of  a point equidistant from two intersecting lines is the angle bisector of  the angle made by these lines. And both the angle bisectors always makes a right angle.

■ If the bisector of  ∠B and  ∠C of  a quadrilateral ABCD intersect in P, then P is equidistant from AB and CD.

Best  of  Luck