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Axis
The line over which a parabola is symmetric.
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Branch
The term for each of the two distinct sections of the graph of a hyperbola.
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Center
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.
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Circle
The set of all points equidistant from a given fixed point.
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Conic
The intersection of a plane and a right circular cone.
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Conjugate Axis
The line segment related to a hyperbola of length 2b whose midpoint is the center.
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Degenerate Conic
A conic which is not a parabola, ellipse, circle, or hyperbola. These include lines, intersecting lines, and points.
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Diameter
A line segment that contains the center of a circle whose endpoints are both on the circle, or sometimes, the length of that segment.
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Directrix
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.
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Eccentricity
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.
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Ellipse
The set of all points such that the sum of the distances from the point to each of two fixed points is constant.
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Focus
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.
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Hyperbola
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.
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Major Axis
The line segment containing the foci of an ellipse whose endpoints are the vertices whose length is 2a.
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Minor Axis
The line segment containing the center of an ellipse perpendicular to the major axis whose length is 2b.
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Parabola
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.
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Radius
A segment between the center of a circle and a point on the circle, or sometimes, the length of that segment.
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Transverse Axis
The line segment that contains the center and whose endpoints are the two vertices of a hyperbola.
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Vertex
(Plural = "vertices") 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.
Terms
Formulae
Polar Form of a Conic | r = ![]() ![]() |
Standard Form of a Circle | The standard equation for a circle is (x - h)2 + (y - k)2 = r2. The center is at (h, k). The radius is r. |
Standard Form of an Ellipse |
The standard equation of an ellipse with a horizontal major axis is the
following:
![]() ![]() ![]() ![]() |
Standard Form of a Hyperbola |
The standard equation for a hyperbola with a horizontal transverse axis
is ![]() ![]() ![]() ![]() |
Standard Form of a Parabola | If a parabola has a vertical axis, the standard form of the equation of the parabola is this: (x - h)2 = 4p(y - k), where p≠ 0. The vertex of this parabola is at (h, k). The focus is at (h, k + p). The directrix is the line y = k - p. The axis is the line x = h. If a parabola has a horizontal axis, the standard form of the equation of the parabola is this: (y - k)2 = 4p(x - h), where p≠ 0. The vertex of this parabola is at (h, k). The focus is at (h + p, k). The directrix is the line x = h - p. The axis is the line y = k. |