Locus (11.111.3)
Understand the concept of loci

TheoryIn geometry, a locus is a set of points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.

Examples

Solutions
Describe and sketch the locus of points satisfying given conditions

ExamplesSquare ABCD is rotated about its vertex C. Sketch and describe the locus of vertex A.

Solutions
The locus of B is a circle with the centre at D and BD as its radius.
Describe the locus of points with algebraic equations

ExamplesIt is given that a moving point P is equidistant from A(2, 0) and B(3,5).
(a) Draw and describe the locus of P.
(b) Find the equation of the locus of P.

Solutions
(a) The locus of P is the perpendicular bisector of AB.
(b) Let (x, y) be the coordinates of the moving point P.
\(AP = \sqrt {{{[x  (  2)]}^2} + {{(y  0)}^2}} \) units
\( = \sqrt {{{(x + 2)}^2} + {y^2}} \) units
\(BP = \sqrt {{{(x  3)}^2} + {{[y  (  5)]}^2}} \) units
\( = \sqrt {{{(x  3)}^2} + {{(y + 5)}^2}} \) units
Therefore, the equation of the locus of P is \(x  y  3 = 0\).