Conic sections

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting two points on the circle and passing through the centre is called the diameter. A circle bounds a region of the plane called a disc.

thumb|right|upright=1.36|Part of a parabola (blue), with various features (other colours). The complete parabola has no endpoints. In this orientation, it extends infinitely to the left, right, and upward. thumb|The parabola is a member of the family of conic sections.

curve obtained by intersecting a cone and a plane

thumb|A hyperbola is an open curve with two branches, the intersection of a plane (geometry)|plane with both halves of a double cone. The plane does not have to be parallel to the axis of the cone; the hyperbola will be symmetrical in any case.|alt=The image shows a double cone in which a geometrical plane has sliced off parts of the top and bottom half; the boundary curve of the slice on the cone is the hyperbola. A double cone consists of two cones stacked point-to-point and sharing the same axis of rotation; it may be generated by rotating a line about an axis that passes through a point of

eccentricity of a conic section

In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the roots without computing them. More precisely, it is a polynomial function of the coefficients of the original polynomial. The discriminant is widely used in polynomial factoring, number theory, and algebraic geometry.

theorem

fixed reference point; special points with reference to which any of a variety of curves is constructed

theorem that the three long diagonals of a hexagon that is tangent to a conic section meet in a single point

term in geometry; longest and shortest semidiameters of an ellipse

mathematical concept

quantity describing conic sections

term in trigonometry

geometric figure

theorem of 2D geometry

Geometric relationship between the zeros of a cubic polynomial and of its derivative

conic sections with the same foci

theorem in Euclidean geometry

Perpendicular diameters of a conic section

Determine an orbit from two position vectors and the time of flight