An ellipse is also the locus of all points of the plane whose distances to two fixed points add to the same constant.

The characterization of an ellipse as the locus of points so that sum of the distances to the foci is constant leads to a method of drawing one using two drawing pins, a length of string, and a pencil.

The locus of these points would not be a supply curve in any conventional sense.

In analytic geometry, a sphere with center ( x < sub > 0 </ sub >, y < sub > 0 </ sub >, z < sub > 0 </ sub >) and radius r is the locus of all points ( x, y, z ) such that

It is the fundamental plane of the horizontal coordinate system, the locus of points that have an altitude of zero degrees.

Thus the IS curve is a locus of points of equilibrium in the " real " ( non-financial ) economy.

The radio horizon is the locus of points at which direct rays from an antenna are tangential to the surface of the Earth.

It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity.

A terminator is defined as the locus of points on a Moon or planet where the line through a Sun is tangent.

* Streaklines are the locus of points of all the fluid particles that have passed continuously through a particular spatial point in the past.

It is known that if the Hodge conjecture is true, then the locus of all points on the base where the cohomology of a fiber is a Hodge class is in fact an algebraic subset, that is, it is cut out by polynomial equations.

In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points F < sub > 1 </ sub > and F < sub > 2 </ sub >, known as foci, at distance 2a from each other as the locus of points P so that PF < sub > 1 </ sub >· PF < sub > 2 </ sub > = a < sup > 2 </ sup >.

The lemniscate was first described in 1694 by Jakob Bernoulli as a modification of an ellipse, which is the locus of points for which the sum of the distances to each of two fixed focal points is a constant.

A Cassini oval, by contrast, is the locus of points for which the product of these distances is constant.

An algebraic curve defined over a field F may be considered as the locus of points in F < sup > n </ sup > determined by at least n − 1 independent polynomial functions in n variables with coefficients in F, g < sub > i </ sub >( x < sub > 1 </ sub >, …, x < sub > n </ sub >), where the curve is defined by setting each g < sub > i </ sub > = 0.

It is often desirable to consider that curves are a locus of points in projective space.

If the field F is not algebraically closed, the point of view of function fields is a little more general than that of considering the locus of points, since we include, for instance, " curves " with no points on them.

If the base field F is the field R of real numbers, then x < sup > 2 </ sup > + y < sup > 2 </ sup > = − 1 defines an algebraic extension field of R ( x ), but the corresponding curve considered as a locus has no points in R. However, it does have points defined over the algebraic closure C of R.

The radius of the largest ball about the origin in T < sub > p </ sub > M that can be mapped diffeomorphically via exp < sub > p </ sub > is called the injectivity radius of M at p. The cut locus of the exponential map is, roughly speaking, the set of all points where the exponential map fails to have a unique minimum.

The input plane is defined as the locus of all points such that z

The output plane is defined as the locus of all points such that z =

For example, a circle may be defined as the locus of points in a plane at a fixed distance from a given point.

The ramification locus of the double cover is a plane curve C of degree 6, and all the nodes of K which are not p map to nodes of C.

The locus where the orientifold action reduces to the change of the string orientation is called the orientifold plane.

If ( as is often done ) one takes the definition of the ellipse to be the locus of points P such that d ( F < sub > 1 </ sub >, P ) + d ( F < sub > 2 </ sub >, P ) = a constant, then the argument above proves that the intersection of a plane with a cone is indeed an ellipse.

The astroid is a real locus of a plane algebraic curve of genus zero.

For a plane curve C and a given fixed point P, the pedal curve of C is the locus of points X so that PX is perpendicular to a tangent to the curve passing through X.

For instance, the locus of the moon when the earth is at perihelion is a recurrence plot ; the locus of the moon when it passes through the plane perpendicular to the Earth's orbit and passing through the sun and the earth at perihelion is a Poincaré map.

Linear systems may or may not have a base locus – for example, the pencil of affine lines has no common intersection, but given two ( nondegenerate ) conics in the complex projective plane, they intersect in four points ( counting with multiplicity ) and thus the pencil they define has these points as base locus.

In three dimensions, the locus of points equidistant from two given points is a plane, and generalising further, in n-dimensional space the locus of points equidistant from two points in n-space is an ( n − 1 )- space.

One simple definition of the ellipse is the " locus of all points of the plane whose distances to two fixed points ( called the foci ) add to the same constant ".

The locus of horopteric points in this plane takes the form of the arc of a circle ( the Vieth-Müller circle ) going from one nodal point to the other in space, passing through the fixation point.

are the coordinates of points A, B, and C. The circumcircle is then the locus of points v = ( v < sub > x </ sub >, v < sub > y </ sub >) in the Cartesian plane satisfying the equations

A Cassini oval is a quartic plane curve defined as the set ( or locus ) of points in the plane such that the product of the distances to two fixed points is constant.

It is now known that each of the A, B, and O alleles is actually a class of multiple alleles with different DNA sequences that produce proteins with identical properties: more than 70 alleles are known at the ABO locus.

Other disorders are also due to recessive alleles, but because the gene locus is located on the X chromosome, so that males have only one copy ( that is, they are hemizygous ), they are more frequent in males than in females.

Among other genetic information the F-plasmid carries a tra and trb locus, which together are about 33 kb long and consist of about 40 genes.

" However, the locus of the celebrations is the national capital, Ottawa, Ontario, where large concerts and cultural displays are held on Parliament Hill, with the governor general and prime minister typically officiating, though the monarch or another member of the Royal Family may also attend or take the governor general's place.

Other researchers believe that individuals with an internal locus of control-that is, people who believe that the gambling outcomes are the result of their own skill-are more susceptible to the gambler's fallacy because they reject the idea that chance could overcome skill or talent.

If the DNA sequence at a particular locus varies between individuals, the different forms of this sequence are called alleles.

In these species, haploids are male and diploids heterozygous at the sex locus are female, but occasionally a diploid will be homozygous at the sex locus and develop as a male instead.

Because these basic ontological meanings both generate and are regenerated in everyday interactions, the locus of our way of being in a historical epoch is the communicative event of language in use.

The attempt was abandoned in the 1990s with the result that the political leadership within the state are also the leaders of the party, thereby creating a single centralized locus of power.

The locus classicus of the 18th-century portrayal of the American Indian are the famous lines from Alexander Pope's " Essay on Man " ( 1734 ):

By sharing data, corpus linguists are able to treat the corpus as a locus of linguistic debate, rather than as an exhaustive fount of knowledge.

As there are often many alleles present at a microsatellite locus, genotypes within pedigrees are often fully informative, in that the progenitor of a particular allele can often be identified.

With the abundance of PCR technology, primers that flank microsatellite loci are simple and quick to use, but the development of correctly functioning primers is often a tedious and costly process. A number of DNA samples from specimens of Littorina plena amplified using polymerase chain reaction with primers targeting a variable simple sequence repeat ( SSR, a. k. a. microsatellite ) locus.

If positive clones can be obtained from this procedure, the DNA is sequenced and PCR primers are chosen from sequences flanking such regions to determine a specific locus.

Because the 13 loci that are currently used for discrimination in CODIS are independently assorted ( having a certain number of repeats at one locus doesn't change the likelihood of having any number of repeats at any other locus ), the product rule for probabilities can be applied.