An<unk>  is a type of conic section: if a conical surface is cut with a plane which does not intersect the cone's base, the intersection of the cone and plane is an<unk> .  For a short elementary proof of this, see Dandelin spheres.
Algebraically, an<unk>  is a curve in the Cartesian plane defined by 
an equation of the form
such that '"`UNIQ--postMath-00000002-QINU`"', where all of the coefficients are real, and where more than one solution, defining a pair of points (x, y) on the<unk> , exists.
An<unk>  can be drawn with two pins, a loop of string, and a pencil. The pins are placed at the foci and the pins and pencil are enclosed inside the string. The pencil is placed on the paper inside the string, so the string is taut. The string will form a triangle. If the pencil is moved around so that the string stays taut, the sum of the distances from the pencil to the pins will remain constant, satisfying the definition of an<unk> .
The line segment AB, that passes through the foci and terminates on the<unk> , is called the major axis.  The major axis is the longest segment that can be obtained by joining two points on the<unk> . The line segment CD, which passes through the center (halfway between the foci), perpendicular to the major axis, and terminates on the<unk> , is called the minor axis. The semimajor axis (denoted by a in the figure) is one half the major axis: the line segment from the center, through a focus, and to the edge of the<unk> . Likewise, the semiminor axis (denoted by b in the figure) is one half the minor axis.
If the two foci coincide, then the<unk>  is a circle; in other words, a circle is a special case of an<unk> , one where the eccentricity is zero.
An<unk>  centered at the origin can be viewed as the image of the unit circle under a linear map associated with a symmetric matrix '"`UNIQ--postMath-00000003-QINU`"', '"`UNIQ--postMath-00000004-QINU`"' being a diagonal matrix with the eigenvalues of '"`UNIQ--postMath-00000005-QINU`"', both of which are real positive, along the main diagonal, and '"`UNIQ--postMath-00000006-QINU`"' being a real unitary matrix having as columns the eigenvectors of '"`UNIQ--postMath-00000007-QINU`"'. Then the axes of the<unk>  will lie along the eigenvectors of '"`UNIQ--postMath-00000008-QINU`"', and the eigenvalues are the lengths of the semimajor  and semiminor axes.
An<unk>  can be produced by multiplying the x coordinates of all points on a circle by a constant, without changing the y coordinates. This is equivalent to stretching the circle out in the x-direction.
Ellipse
Burial
Bedwetting
Strangling
Stripping
Web colors
Lateral thinking
Punctuation