Conic

Conic Section - Properties
... points determine a line, five points determine a conic ... in general linear position, meaning no three collinear, there is a unique conic passing through them, which will be non-degenerate this is true over both the affine plane and ... Indeed, given any five points there is a conic passing through them, but if three of the points are collinear the conic will be degenerate (reducible, because it contains a line), and may not be ...

Conic Optimization
... Conic optimization is a subfield of convex optimization that studies a class of structured convex optimization problems called conic optimization problems ... A conic optimization problem consists of minimizing a convex function over the intersection of an affine subspace and a convex cone ... The class of conic optimization problems is a subclass of convex optimization problems and it includes some of the most well known classes of convex optimization problems, namely linear and semidefinite ...

Conic Section
... In mathematics, a conic section (or just conic) is a curve obtained as the intersection of a cone (more precisely, a right circular conical surface) with a plane ... In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2 ... One of the most useful, in that it involves only the plane, is that a conic consists of those points whose distances to some point, called a focus ...

Conic Section - See Also
... Conic Sections Rebellion Dandelin spheres Director circle Elliptic coordinates Focus (geometry), an overview of properties of conic sections related ...

Conic Section - Homogeneous Coordinates
... In homogeneous coordinates a conic section can be represented as Or in matrix notation The matrix is called the matrix of the conic section ... is called the determinant of the conic section ... If Δ = 0 then the conic section is said to be degenerate this means that the conic section is either a union of two straight lines, a repeated line, a ...