Until the beginning of the 20th century, a geometrical shape (for example a curve) was not considered as an infinite set of points; rather, it was … See more

Examples from plane geometry include:
• The set of points equidistant from two points is a perpendicular bisector to the line segment See more

To prove a geometric shape is the correct locus for a given set of conditions, one generally divides the proof into two stages: the proof that all … See more

First example
Find the locus of a point P that has a given ratio of distances k = d1/d2 to two given points.
In this example k = 3, A(−1, 0) and B(0, 2) are chosen as the fixed points.
P(x, y) is a point of … See more

• Algebraic variety
• Curve
• Line (geometry)
• Set-builder notation See more