Two pencils are called homographic if their lines are in a 1-1 correspondence that preserves the cross-ratio. The intersections of the corresponding lines of two homographic pencils form a conic that passes through the two pencil vertices. (There is a restriction that the line through the vertices does not correspond to itself.) One way to obtain homographic pencils is to move a point on a conic (a straight line, in particular). The point is connected to two fixed points - vertices of two pencils. The corresponding lines of the two pencils are inclined at fixed angles to the two "generating" lines that join the vertices to the variable point.
