Circles and Curves in Perspective
From DT Online
In most drawing methods, including perspective, circles and curves have to be constructed by plotting points using straight lines then sketching through them.
Circles and arcs are drawn in perspective by first using normal projection methods to plot the imaginary square or rectangle that would surround them and then sketching the curve inside it.
To help sketch the circle accurately, its centre can be found by drawing the diagonals of the bounding square. Also the points where the circle touches each side of the (perspective) square can be found by projecting from the centre to the Vanishing Points
Note: The Major Axis of the Ellipse is always at right angles to the axis of the cylinder.