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In Euclidean geometry, all lines are congruent, meaning that every line can be obtained by moving a specific line. However, lines may play special roles with respect to other geometric objects and can be classified according to that relationship. For instance, with respect to a conic (a circle, ellipse, parabola, or hyperbola), lines can be:
An ellipse (red) obtained as the intersection of a cone with an inclined plane. Ellipse: notations Ellipses: examples with increasing eccentricity. In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.
For example, the first and fourth of Euclid's postulates, that there is a unique line between any two points and that all right angles are equal, hold in elliptic geometry. Postulate 3, that one can construct a circle with any given center and radius, fails if "any radius" is taken to mean "any real number", but holds if it is taken to mean ...
Line; Degree 2. Plane curves of degree 2 are known as conics or conic sections and include Circle. Unit circle; Ellipse; Parabola; Hyperbola. Unit hyperbola; Degree 3
The circle is a special kind of ellipse, although historically Apollonius considered it a fourth type. Ellipses arise when the intersection of the cone and plane is a closed curve. The circle is obtained when the cutting plane is parallel to the plane of the generating circle of the cone; for a right cone, this means the cutting plane is ...
Several types of curves have the property that all examples of that type are similar to each other. These include: Lines (any two lines are even congruent) Line segments; Circles; Parabolas [14] Hyperbolas of a specific eccentricity [15] Ellipses of a specific eccentricity [15] Catenaries; Graphs of the logarithm function for different bases
Toggle Generally composed of straight line segments subsection. ... (example) Heptagram – star ... Circle. Archimedes' twin circles;
A standard definition of an ellipse is the set of points for which the sum of a point's distances to two foci is a constant; if this constant equals the distance between the foci, the line segment is the result. A complete orbit of this ellipse traverses the line segment twice. As a degenerate orbit, this is a radial elliptic trajectory.