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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