Chapter 10 - Section 1: The Circle
by Chris A (ICM 5th period)
Key Terms:
| Locus | a set of points that satisfy a given condition |
| Circle | a locus in which all points are the same distance from one common center |
| Radius | the distance from the center to any point on the circle |
Circles that have the same center, but not the same radius, are concentric circles.
The standard form of the equation of a circle is
(x-h)2 + (y-k)2 = r2
where (h , k) is the center and r is the radius.
The general form of the equation of a circle is
x2 + y2 + Dx + Ey + F = 0
where D, E, and F are constants.
Little Johnny just got a new amp. He knows that when he plays his guitar, it's loud enough to be heard 7 houses away in every direction. Looking at a map of his neighborhood, he realizes that the houses and streets are arranged in a grid. If there is one house per grid square, how many neighbors will call his parents? Also, graph Little Johnny's zone of neighborly anger.
Find the standard form of the equation with a center at (-5, 1) and a radius of 7.
| (x-h)2 + (y-k)2=r2 | Standard form |
| (x+5)2 + (y-1)2=49 | Substitute (-5,1) for center (h,k) and 49 for r2 |
Now graph.
Area of a circle = pr2
7x7=49 x p= 153.93804 One unit is one house. This decimal means part of a house can hear Little Johnny. Since you can't have 0.93804 of a house, we can assume that the whole house can hear him.
Little Johnny's parents will be called 154 times by angry neighbors asking him to stop playing guitar and learn how to hum instead (or play the kazoo).
Visit Math2.org to learn more about circles.
www.math2.org/math/geometry/circles.htm - Circles page.
Click here to experience more of Little Johnny's* music.
*Little Johnny didn't actually write any music. It was done by the author of this webpage. Go listen to the music, it's good for you.
"The
true test of character is not how much we know how to do, but how we behave when
we don't know what to do."
-John Holt
"Bluntness
is a virtue."
-Allison Ling
"Men
are born ignorant, not stupid. They are made stupid by education."
-Bertrand Russell
"One morning I shot an elephant in my pajamas. How he got into my pajamas I'll never know."
-Groucho Marx
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