Commonly studied loci 
All conic sections are all loci:
- Parabola: the set of points equidistant from a single point (the focus) and a line (the directrix).
- Hyperbola: the set of points for each of which the absolute value of the difference between the distances to two given foci is a constant.
- Ellipse: the set of points for each of which the sum of the distances to two given foci is a constant. In particular, the circle is a locus.
Straight lines are loci too: every straight line is the set of all points equidistant to two given points.
Consider the locus of all points P such that its distance from the point (−1,0) is three times its distance from the point (0,2). If P = (x,y), then, saying that P belongs to the locus means that
This is equivalent to
This equation represents a circle.
See also 
- Robert Clarke James, Glenn James: Mathematics Dictionary. Springer 1992, ISBN 978-0-412-99041-0, p. 255 (restricted online copy at Google Books)
- Alfred North Whitehead: An Introduction to Mathematics. BiblioBazaar LLC 2009 (reprint), ISBN 978-1-103-19784-2, pp. 121 (restricted online copy at Google Books)
- George Wentworth: Junior High School Mathematics: Book III. BiblioBazaar LLC 2009 (reprint), ISBN 978-1-103-15236-0, pp. 265 (restricted online copy at Google Books)
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