A locus is the term used to describe the path of a single moving point that obeys certain conditions. The point A above will move around the origin at a distance 2 units away, depicted by the circle. Similarly, just like a compass, the path of a pencil is a circle with centre at the point of the compasses.
This study relates to distances between a point and a line, line and another line, or even a point to a point! Use the distance and perpendicular distance formula to solve problems relating to loci (plural form of locus).
1. Find the equation of the locus of a point P(x, y) that moves so that is always 3 units from the origin.
2. Find the equation of the locus of point P(x, y) that moves so that the distance PA to distance PB is in the ratio 2:1 where A=(-3, 1) and B=(2, -2).
Using Geogebra App, the trajectory of the locus is shown below:
3. Find the equation of the locus of point P(x, y) that is equidistant from a fixed point A(1, -2) and fixed line with equation y=5.
Circle as Locus
The circle with centre (a, b) and radius r, has the equation:
Hence, the circle with a centre at the origin has the equation:
1. Find the equation of the locus of a point that is always 2 units from the point (-1, 0).
2. Find the radius and the coordinates of the centre of the circle: