Thursday, December 13, 2007

Ellipses

Well it's Miller again scribing my last scribe for the year. After this I wont have to worry about scribing again.

Today was a very charismatic class. In the morning class we learned that Mr. K's favorite channel on television was channel 50(tree house). Apparently it is the most educational show... only if Steve was still there. Anywhoo today we continued to learn about ellipses.

Mr.K showed told us about the whisper room. How it works. If we stand at focal point in the room and someone were to whisper while they were at the other focal point we
would hear what they'd say. He then becamce " Ultraman" and took his great and mighty sword and cut the Whisper room in half to show us how our sound would travel around.



In this picture Mr. K hath spliced the room in half. We are looking at it from a horizontal point of view. The red lines represent the voices of the two people sitting at the points marked on ellipse. These are also known as "focal radii".

We then were taught how to properly sketch an ellipse. In the picture below. I believe that it was jessica and lina who wonderfully completed this question on the board.



To draw this ellipse fully we first must find out where the center is and find the focal points.

As we look at the equation we can easily find the center of the ellipse which is (2,-1). We get this by looking for the "h" and the "k" of the equation.

To find the focal point we have to find what C is. C is the distance from the center to one of the focal points. To find this we use pythagorean theorem.

c^2=a^2-b^2 c^2=16-9 c^2=7 c=√7

Once we have this we move √7 units up from the center and √7 units down, since this ellipse opens vertically. That means the focal points of the ellipse are (2,√7-1) and (2,-1-√7).

The length of the major axis is 8. To find this we take whatever "a" was in the equation and multiply it by two. In this case "a" was 4. So we go 2x4=8.

Similarly to find the minor axis we take "b" and multiply by two. Which is 2x3=6.


AFTERNOON CLASS*

Our afternoon class was cut short to an extent. We found out that it was BLOG's birthday and we ended up singing happy birthday 3 times and NONE of them were saved!!. Sigh.. Neways..
In the afternoon we changed an equation from standard form to general form.




To turn the equation from standard form into general form we must first make every term be over the same denominator. In this particualr problem we made everything over the common denominator of 400. After that we expanded the equation and allowed it to equal zero. Then after we combined the like terms we have found the "general form" for ellipses.

*NOTE. Here are some tips to find out if an equation shows a circle, ellipse or a parabola.
- two squared terms means it may be a circle or an ellipse.
-for it to be an ellipse the coefficients on the x and y terms MUST NOT be equal. If so it is a circle.
- If only one term is squared then it is a parabola. If the x is squared it is a vertical parabloa and if the y is squared it is a horizontal parabola.

That's what we did for the first half of the second class. Then the other half we spent wishing WEBBLOGGING happy birthday. "HAPPYBIRTHDAY WEBLOGGING" This was most of the information that got welded into my brain today. As for tommorows scribe the next scribe is OLIVER.


1 comment:

Lani said...

Hi Miller,

It sounds as if you had a great birthday celebration!

Your word choice (charismatic), your description of the whisper room phenomenon and "Ultraman" really draw your reader to your post. You've used to color to highlight important points and notes to assist all your readers.

Very nicely done!

Does lots of information get "welded into your brain" each day in Pre-Cal?

Best,
Lani