Chapter 10, Section 4
*hYpErBoLaS!*
Sarah B.
ICM
Billy and Katie are an ice-skating pair and they are trying to come up with a new routine. Katie suggests that they start out in the middle of the ice, and then skate to opposite corners. She then suggests that they each skate a small semi-circle. Billy loves Katie's idea for the beginning of their routine. He decides to draw their routine on a piece of paper, and he realizes that it looks just like a hyperbola. Since accuracy is extremely important in ice-skating, Billy and Katie decide to make their routine into an equation, and graph it, so that they know exactly where they should skate.
Billy and Katie know that the ice rink is 64 feet long and 36 feet wide. They decide to make (0,0) the coordinate for the center.
Their next step is to put this information into an equation. The standard form of an equation of a hyperbola is (x-h)2/a2-(y-k)2/b2=1 . The h and k represent the coordinates of the center. Since the center of Billy and Katie's hyperbola is (0,0), the h=0 and they k=0 for their equation. The a is the length of the x-axis between the parts of the hyperbola, and the b is the length of the y-axis of the box.
Their equation is: x2/64-y2/36=1. Their next step is to graph. To graph this equation, Billy and Katie know that they need to put a point at (0,0) for the center. Next, they need to put a point at (8,0) and (-8,0). After that, they put points at (0,6) and (0, -6). They found those coordinates by taking the square roots of a and b and going over that many units on the x and y axis, respectively. Next, they draw a box connected by the points. They then draw in the asymptotes which cut diagonally through the box and go through the center. Since the x comes first in their equation, they know that the hyperbola needs to be turned on its side, with the vertex touching the coordinates (-8,0) and (8,0). This is what their graph looks like:
This
picture was made at http://www.school.discovery.com
By looking at the graph, Billy and Katie now know where to skate for their routine. They will start at the center and then, using the asymptotes, skate to the corners of the ice rink.
The following website also offers help with hyperbola problems:http://www.krellinst.org/UCES/archive/resources/conics/node39.html
“For
those who are always courteous and respectful of elders, four things increase:
life, beauty, happiness and strength.”
-Buddha, The Dhammapada
This quote is about the Character Education Trait, respect. Buddha is saying that if a person is respectful and kind to others, they will live a longer and better life. By respecting others, one earns respect themself.
This quote, and other quotes can be found on this website: http://www.ccmidshore.org/pillars/quotes_respect.html