10-7:
Systems of Second-Degree Equations
and Inequalities
By: David
G., Jr., Esq.
"I
love you like a fat kid loves cake."
- 50 Cent -
- After this lesson, you should be
able to solve systems of second-degree equations and Inequalities
- Thought to have been nearly
extinct for almost 2 decades now, Disco dancers have been sought after for
their valuable photographs by collectors and poachers world-wide. Dan,
a Disco enthusiast, has heard rumors of the rarest of the rare, Disco
Inferno, being spotted in the Triangle (RDU-Chapel Hill). However, he
doesn't know it's exact location. Raleigh (located at (3, -2)), said
Inferno was seen 3 miles away. Chapel Hill, at (-3, -2), placed the
rare specimen 3 miles from the city. Durham is at (0, 3) on the NC
map, and the saw Disco Inferno 5 miles away. However, none of the
cities reported in which direction they were looking when they spotted the
dancer. But that didn't matter to Dan. He knew he could as you
for help with locating Disco Inferno. Help Dan by making a graph to
represent the Triangle and the possible locations of the specimen, and then
solve to find Inferno's exact location.
- First, plot three points to
represent the cities. Then, since we do not know in which direction
Disco Inferno was, use circles to represent Disco Infernos location, with
his distance from the cities as the radiuses.
- Based on the graph, there is one
solution to the problem.
- Now write equations to for the
three circles:
Raleigh: (x - 3)2
+ (y + 2)2 = 1
9
9
Durham: (x + 3)2 +
(y + 2)2 = 1
9
9
Chapel Hill: x2 +
(y - 3)2 = 1
25 25
- By solving these equations using
elimination, or by simply looking at the graph, we see that Disco Inferno's
exact location is (0, -2).
- Dan went to this location and
got a photograph of the Dancing King. He sold it for millions of
dollars, realized his career of following Disco Dancers around the world was
a waste of time, and retired a rich man.
- For extra help, go to: http://www.mathkal.co.il/tpc_eq2.htm
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