1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Definition of Locus Stage 6 - Year 11 Mathematic (Preliminary)

2 Definition of a locus  Describes the path of a single moving point that obeys certain conditions.

3  The Circle The point is always the same distance from the point ‘O’ O x 2 + y 2 = r 2 Definition of a locus  Describes the path of a single moving point that obeys certain conditions.

4  The Straight line y = mx + b Definition of a locus  Describes the path of a single moving point that obeys certain conditions.

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6 Reuleaux Triangle 1

7 Reuleaux Triangle 2 rotates. First, the path of the boundary is not a square at the four corners. But because the triangle rotates within a square, it is the basis for a square drill bit. The behavior of the center is also fascinating. The center does not remain fixed and thus traces a path composed of four arcs of an ellipse. Observe the path of the triangle as it

8 Ellipse

9 Point rotating on circle

10 The Double Pendulum

11 Pedal Curve  A pedal curve is the locus of the feet of the perpendiculars from the point to the tangents to the given figure.

12 Hypotrochoid  The red curve is traced as the smaller black circle rolls around inside the larger black circle

13 Darts Ballistics Simulator