Thursday, May 28, 2009

BOB for Conics

This unit was extremely short but I learned alot about it. this unit involved graphs like the parabola, ellipse, circle and hyperbola. In order to get these different types of graphs we can cut a double-sided cone( looks like an hour-glass) from different angles. If we cut the top it will create a circle. If we cut at an angle we can create an ellipse. If we cut the bottom it will create a parabola. and also if we cut it at a 90 degree angle down it will create a hyperbola.

The most interesting thing I learned and most useful was the anatomy of the Hyperbola.
This mini box allows us to find the hyperbola with ease and with less information required. Like if you have the conjugate axis and transverse you can find everything else like the asymptotes, vertex and center. Or if you have the slope of the asymptote and know the coordinates of an axis then you can find all the rest of the information also. Hyperbolas involve the difference of distances will always be constant.

((x-h)^2)/(a^2) - ((y-k)^2)/(b^2)

+ or - determines whether its vertical or horizontal. Positive x = horizontal, negative x = vertical.

The ellipse was quite interesting. I was quite amazed that it does not have a radius but instead foci that help determine the value of c. Also within it are the major axis and minor axis. Which help determine the value of a and b in the standard form equation:

((x-h)^2)/(a^2) + ((y-k)^2)/(b^2)

the a and b's are switched in a vertical ellipse.

All in all it was short, but very straight forward. Mr.K said we should see the geometry when we see the equations like in the matrix where it shows code but they see people. I can safely say I'm ready and hope they're no big surprises.