## Part II

**CONSTRUCT A PARABOLA **

GIVEN THE FOCUS AND DIRECTRIX

I feel I** learned the most mathematics** when I did this construction
(assignment 6). This may seem very elementary, and I've seen the construction
a couple of times. But constructing it yourself is much more enlightening.
I was really forced to think about the meaning of the focus and directrix.
It's very easy to say the definition, even to wonderfully explain, the definition
and meaning. Still, I know more now after going through the construction.

This is my **best effort during the quarter. **Due to the new grasp I
have on the information, this knowledge will be most useful to me when teaching.
Not only will my discussions of this be crisper, they also will be more
thorough. And presenting it as a GSP sketch and discussing the way it is
constructed (not just showing the pretty picture) will benefit my students
in the same manner.

You said in class (on more than one occasion) that we should all be able
to make this construction in 3 - 4 minutes. And you always proceeded to
make the construction...in about 2 minutes. When I sat down to construct
the parabola, you voice echoed continuously "...3 - 4 minutes."
I worked and worked and thought and "...3 - 4 minutes." I could
not remember anything about the construction you did, except that you used
a triangle (and "...3 - 4 minutes). Suffice it to say that when I completed
the task (about5 hours) later I felt very **satisfied and incredibly happy**,
elated even.

Still, you may think this too elementary and , after finding out I spent
so much time on it, that I need more help than you originally may have thought.
But what means so much to me is that I struggled to figure out the construction
and I finally did, all alone on a Sunday afternoon. I asked no one anything.
It was wonderful! I am not convinced my construction is the most efficient
yet, yours is a few steps shorter maybe. But as with many paths, longer
and shorter constructions accomplish different things. However, **the problem
opened up new elements of mathematics** for me because I awoke that ability
in me to not only search but accomplish. And I did it alone.

Click **here** to see the GSP construction.

I have attempted about 80% of the work.

I have completed about 80% of the work.

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