1 Flashcards
The line over which a parabola is symmetric.
Axis
The term for each of the two distinct sections of the graph of a hyperbola.
Branch
For an ellipse and hyperbola, the midpoint between the foci. For a circle, the fixed point from which all points on the circle are equidistant.
Center
The set of all points equidistant from a given fixed point.
Circle
The intersection of a plane and a right circular cone.
Conic
The line segment related to a hyperbola of length 2b whose midpoint is the center.
Conjugate Axis
A conic which is not a parabola, ellipse, circle, or hyperbola. These include lines, intersecting lines, and points.
Degenerate Conic
A line segment that contains the center of a circle whose endpoints are both on the circle, or sometimes, the length of that segment.
Diameter
For a parabola, it is the line whose distance from any point on the parabola is the same as the distance from that point to the focus. For a conic defined in polar terms, it is the line whose distance from any point on the conic makes a constant ratio with the distance between that point and the focus.
Directrix
The ratio in an ellipse or hyperbola. Under the polar definition of conics, e is the constant ratio of the distance from a point to the focus and the distance from that point to the directrix.
Eccentricity
The set of all points such that the sum of the distances from the point to each of two fixed points is constant.
Ellipse
For a parabola, the point whose distance from any point on the parabola is the same as the distance between that point and the directrix. For an ellipse, one of two points–the sum of whose distances to a point on the ellipse is constant. For a hyperbola, one of two points–the difference of whose distances to a point on the hyperbola is constant. Under the polar definition of a conic, it is the point whose distance from a point on the conic makes a constant ratio with the distance between that point and the directrix.
Focus
The set of all points such that the difference of the distances between each of two fixed points and any point on the hyperbola is constant.
Hyperbola
The line segment containing the foci of an ellipse whose endpoints are the vertices whose length is 2a.
Major Axis
The line segment containing the center of an ellipse perpendicular to the major axis whose length is 2b.
Minor Axis
The set of all points such that the distance between a point on the parabola and a fixed line is the same as the distance between a point on the parabola and a fixed point.
Parabola
A segment between the center of a circle and a point on the circle, or sometimes, the length of that segment.
Radius
The line segment that contains the center and whose endpoints are the two vertices of a hyperbola.
Transverse Axis
For a parabola, the point halfway between the focus and the directrix. For an ellipse, one of two points where the line that contains the foci intersects the ellipse. For a hyperbola, one of two points at which the line containing the foci intersects the hyperbola.
Vertex
A round conic defined by an eccentricity of 0. Also, a favorite shape for the terminally lost.
Circle
The curves that can be formed by slicing up a double-cone—because who wouldn’t want to slice up a double-cone.
Conic section
A line perpendicular to the line of symmetry of a conic. Like the focus, the directrix is used in defining the conic section. The function and the directrix don’t get along, and so the graph will always curve away from the directrix.
Directrix
A measure of how weird a conic is, by taking the ratio of the focal distance to the distance to one of the vertices e=f/a.
Eccentricity
Conic section with two foci within a closed curve. Defined by eccentricities greater than 0, but less than 1. Where would the Universe and especially NASCAR be without them?
Ellipse
