Locus- (11.1-11.3)

Understand the concept of loci

  • Graph
  • Theory
  • Examples
  • Solutions

Describe and sketch the locus of points satisfying given conditions

  • Examples
    Square ABCD is rotated about its vertex D. Sketch and describe the locus of vertex B.
  • 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

  • Examples
    It 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 \(x - y - 3 = 0\).