<P> Finally, if AB = 0 assume, without loss of generality, that B = 0 and A = 1 to obtain the parabolic cylinders with equations that can be written as: </P> <Dl> <Dd> x 2 + 2 a y = 0 . (\ displaystyle (x) ^ (2) + 2a (y) = 0 .) </Dd> </Dl> <Dd> x 2 + 2 a y = 0 . (\ displaystyle (x) ^ (2) + 2a (y) = 0 .) </Dd> <P> In projective geometry, a cylinder is simply a cone whose apex (vertex) lies on the plane at infinity . If the cone is a quadratic cone, the plane at infinity passing through the vertex can intersect the cone at two real lines, a single real line (actually a coincident pair of lines), or only at the vertex . These cases give rise to the hyperbolic, parabolic or elliptic cylinders respectively . </P>

What is the shape of the base of a cylinder