This configuration also exists in the graph of an inconsistent system of two linear equations--that outcome arises when the two lines have the same slope.
In hyperbolic geometry there are two forms of this geometric configuration, ultra and limiting. In Euclidean ge- ometry it is the degenerate conic section found by the limiting case as the focal distance goes to infinity while the verti- ces remain constant of a hyperbola. This degenerate conic can also be seen as the intersection of a plane and double cone when the vertex of the cone is moved to a point at infinity making the cone into a cylinder. In projective geome- try, this configuration cannot exist. Solutions in the coordinate plane to the equation y squared equals one provide an algebraic description to this configuration. This configuration also exists in the graph of an inconsistent system of two linear equations--that outcome arises when the two lines have the same slope. Identify this relationship between two lines in the same plane that never intersect.
In hyperbolic geometry there are two forms of this geometric configuration, ultra and limiting.
{parallel} lines