conische

Conische is a term used in Dutch and related languages to describe things relating to cones. In geometry, conic sections are produced by intersecting a plane with a double-napped cone. The study of conische shapes includes the circle, ellipse, parabola, and hyperbola, each with distinct geometric properties and equations.

Conic sections are commonly classified by eccentricity, a measure of how much the shape deviates from a circle. A circle is a special case with eccentricity e = 0; an ellipse has 0 < e < 1; a parabola has e = 1; and a hyperbola has e > 1. The focus-directrix property further characterizes these curves, linking their geometry to distances from a fixed point (focus) and a fixed line (directrix).

A general description of a conic in Cartesian coordinates is given by a second-degree equation: Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, with the discriminant B^2 − 4AC determining the type. Standard forms include the circle x^2 + y^2 = r^2; the ellipse (x^2)/a^2 + (y^2)/b^2 = 1; the parabola y = ax^2 + bx + c; and the hyperbola (x^2)/a^2 − (y^2)/b^2 = 1, each arising from specific plane–cone intersections.

Applications of conische shapes include celestial mechanics and orbital trajectories, optics and lens design, and computer graphics for rendering rounded and reflective shapes. The term also appears in linguistic contexts as the descriptive adjective for cone-related concepts in geometry. See also conic section, circle, ellipse, parabola, hyperbola.