Starting with your cylinders around arbitrary minor axes, you've approached the challenge itself quite well - you've been fastidious in checking the alignment of your ellipses (pencil for your line extensions, while not ideal, is still acceptable because that step is all about analyzing and so we're less concerned with how the choice of tool there would actually influence your linework), and I can see cases like here where you've caught a fairly minor deviation. This is good, because it shows your willingness not to simply accept that "oh I'm close enough, so I may as well mark it as correct", but rather that you are identifying even small issues so that you can continue to improve upon them without plateauing.

While you're applying the elements of this section of the challenge well, I am a little concerned about the slight signs of hesitation I'm seeing in your work. They're quite subtle, but if we look closely, I'm getting the impression from both the slight wobbling in some of your lines, and more notably from the unevenness of many of your ellipses, that you may not be appropriately applying the ghosting method to all of your freehanded marks. Remember - the ghosting method is all about committing most of our time to the planning and preparation phases, so we can ultimately execute that mark with confidence so as to maintain consistent trajectories and even, smooth shapes. It is not uncommon for students to slip off the wagon so to speak, and end up putting less time into their planning and preparation. In turn, they compensate by giving themselves more time to execute the mark, which ultimately reverses the priorities laid out in Lesson 1, resulting in more hesitation and a greater focus on accuracy over flow. Long story short - be sure to review the ghosting method and be sure to apply it consistently for every freehand mark throughout the rest of this course.

Carrying onto your cylinders in boxes, your work here is coming along well, with just a couple things that stood out to me. This exercise is really all about helping develop students' understanding of how to construct boxes which feature two opposite faces which are proportionally square, regardless of how the form is oriented in space. We do this not by memorizing every possible configuration, but rather by continuing to develop your subconscious understanding of space through repetition, and through analysis (by way of the line extensions).

Where the box challenge's line extensions helped to develop a stronger sense of how to achieve more consistent convergences in our lines, here we add three more lines for each ellipse: the minor axis, and the two contact point lines. In checking how far off these are from converging towards the box's own vanishing points, we can see how far off we were from having the ellipse represent a circle in 3D space, and in turn how far off we were from having the plane that encloses it from representing a square.

Ultimately this means that ensuring that we're following the line extension approach correctly, so as to glean as much information on how we can adjust our approach for the next page as we can. I noticed that where it comes to the boxes' line extensions, and extending the contact point lines of the ellipse on either end, you were generally pretty consistent. I did notice at least one case where you neglected one set of the contact point line extensions, but this did not appear to be a pattern.

What was a more consistent pattern however was that you more often appeared to skip over defining the actual minor axis lines for your ellipses. Each ellipse has three lines that need to be extended in order to be compared to the box's vanishing points - two contact points lines, and one minor axis line. Each of these needs to be extended all the way back, and when one or more are missed, it leaves us an opportunity for mistakes to accumulate unnoticed - meaning our partial analysis may not identify those issues, leaving us without awareness of these areas in which we can further improve.

So, be sure to apply those line extensions in their entirety as you move forwards, and as mentioned for the previous section, be sure to use the ghosting method in its entirety as well. I'll go ahead and mark this challenge as complete, and will leave you to address those yourself in your own warmups.