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Each curve in this example is a locus defined as the conchoid of the point P and the line l.In this example, P is 8 cm from l. In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.
The zero-locus of f (x, y) is the set of points in A 2 on which this function vanishes: it is the set of all pairs of complex numbers (x, y) such that y = 1 − x. This is called a line in the affine plane. (In the classical topology coming from the topology on the complex numbers, a complex line is a real manifold of dimension two.)
Locus (mathematics), the set of points satisfying a particular condition, often forming a curve; Root locus analysis, a diagram visualizing the position of roots as a parameter changes; Locus (archaeology), the smallest definable unit in stratigraphy; Locus (genetics), the position of a gene or other significant sequence on a chromosome
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.
It is the locus corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line that rotates with constant angular velocity. Equivalently, in polar coordinates ( r , θ ) it can be described by the equation r = b ⋅ θ {\displaystyle r=b\cdot \theta } with real number b .
The evolute of a curve (blue parabola) is the locus of all its centers of curvature (red). The evolute of a curve (in this case, an ellipse) is the envelope of its normals. In the differential geometry of curves, the evolute of a curve is the locus of all its centers of curvature. That is to say that when the center of curvature of each point ...
A conic is defined as the locus of points for each of which the distance to the focus divided by the distance to the directrix is a fixed positive constant, called the eccentricity e. If 0 < e < 1 the conic is an ellipse, if e = 1 the conic is a parabola, and if e > 1 the conic is a hyperbola.
where K is kept constant, then the locus of P is a circle centered at N with a radius . As P approaches N the locus of P for the corresponding constant K, collapses onto N the nine-point center. Furthermore the nine-point circle is the locus of P such that