course Mth 275
Section 10.2:I didn? have a particular difficulty with the material in this section?t? pretty straightforward and clear. The only problem I had with the problem set was drawing some of the surfaces. The ?rawing Lessons?in the section use angular relationships between the axes that are different from the illustrations of the surfaces later in the section. Eventually I figured out that the layout used in the illustrations of the surfaces made it much easier to visualize and draw the surfaces. Problem 10.2-15 (matching x^2/2 ?y^2/4 + z^2/9 = 1 with the appropriate illustration) initially gave me some difficulty? had no problem concluding that the equation represented a hyperboloid of one sheet, but I took me a while to realize that the matching illustration showed only portions of the surface.
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Bottom line: the math in the section wasn? a problem; drawing the planes and surfaces was a little more of a challenge. I checked the odd-numbered problems with the key in the back of the book, and I? confident that my solutions to the even-numbered problems are correct.
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Looks like you're in good shape.
A couple of words to the wise:
Always check out the coordinate-plane intersections (i.e., the x-y plane, checked by setting z = 0; and the x-z and y=z planes).
It can also be helpful to check out planes parallel to these (e.g., the plane z = c, which is parallel to the x-y plane).
The intersection of a quadric surface with any plane will be a conic section, or will be empty.