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Thursday, May 12, 2005

The Muddiest Point

Most of you seem to have a good grasp of the ellipse! Fantastic! If you need any help with your ellipse homework you can find it here.

By far the muddiest point in our class seems to be the parabola. Here you can play with the parabola as it's defined from the locus definition (which is what we're studying). Play with the java applets, there are two of them, to get a sense of the role "p" plays in the geometry of the parabola.

IMPORTANT: "p" is half the distance between the focus and the directrix when they are perfectly aligned vertically. By dragging the point "B" along the directrix you will sketch out a parabola. Look for when the point "P" is on top of the point "A".

The second applet will show you what happens when you move the focus around. We will discuss these things in class tomorrow, so even if this doesn't entirely make sense to you right now play with the applets so that you will understand what we're talking about in class. ;-)

There were a couple of other questions that came up in our Muddiest Point exercise:

  • about circles
  • arithmetic series
  • changing from general to standard form and back again

We'll be talking lots more about that last point. Please speak to me one-on-one about the first two -- there were only about 3 of you that were feeling muddy about them. ;-)

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