Editing Cylinder (section)

=== Elliptic cylinder ===
If {{math|''AB'' > 0}} this is the equation of an ''elliptic cylinder''.{{sfn|Albert|2016|p=74}} Further simplification can be obtained by [[translation of axes]] and scalar multiplication. If <math>\rho</math> has the same sign as the coefficients {{mvar|A}} and {{mvar|B}}, then the equation of an elliptic cylinder may be rewritten in [[Cartesian coordinates]] as:
<math display=block>\left(\frac{x}{a}\right)^2+ \left(\frac{y}{b}\right)^2 = 1.</math>
This equation of an elliptic cylinder is a generalization of the equation of the ordinary, ''circular cylinder'' ({{math|1=''a'' = ''b''}}). Elliptic cylinders are also known as ''cylindroids'', but that name is ambiguous, as it can also refer to the [[Plücker conoid]].

If <math>\rho</math> has a different sign than the coefficients, we obtain the ''imaginary elliptic cylinders'':
<math display=block>\left(\frac{x}{a}\right)^2 + \left(\frac{y}{b}\right)^2 = -1,</math>
which have no real points on them. (<math>\rho = 0</math> gives a single real point.)