Monday, May 12, 2008

Bit of Review and...Origami?

Highlights for today's class are:
-Reviewing how to write equations of a parabola when given the vertex, focus, and directrix.
-Reviewing what we learned about circles from last class
-Origami-ish fun with circles!

This slide was basically a review from last class to see if we really understood the concepts.

When given the vertex and focus, it is easier to draw a sketch of the parabola first to see which way it opens. Once you know whether it opens in a vertical or horizontal way, you will be able to see which equation you should use (either the horizontal or vertical equation).

P equals the coordinate value that represents whether the equation has the y side squared or the x side squared. In the first question where the focus is (4,0), the P value would equal 4 since the x side is squared and the parabola also opens horizontally. To find what 4P is in the equation, just multiply the P value by 4. Also, if the parabola opens in a negative way, 4P will also be negative.

More review from last class. Since the distance between P and F is equal to the radius, we can use the distance formula to find the standard form for the equation of a circle.

We already did the question on the left side last class, so we worked on the one on the right. We were asked to put it in the standard form (circle). After solving it, questions arose about what to do with -2 since the squareroot of -2 is basically an imaginary number. We came to the conclusion that it wasn't a circle since you can't have a negative value for the radius, thus the not a circle.

*Gasp* A circle with two dots on it...and a doodle I made because I was bored. We were all given a sheet of blank paper and were told to draw a perfectly round circle on it. Then we added the center dot and another dot out on the side somewhere near the circumference. After that we made many ticks on the circumference (minimum 25) and made sure that we clumped the ticks together around the outer dot. We then folded our ticks onto the outer dot. The end result was an elipse on the back side of the paper.

Homework is the above slide. Place points P, Q, and R anywhere on the outside of the elipse. Draw a line connecting them to F1 and F2. Add them together as shown and see what happens ;D

Yep, I joined the advertising bandwagon! Watch Batman: The Dark Knight on July 18 (R.I.P. Heath Ledger)! XD......Okay..time for next scribe. Looks like a new cycle! I choose........Richard. Ahah, well then I'm off! Oh and vote for Joseph for vice president! K, have fun ;D

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