Algebra 2 Graphing Circles
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Round One
Graphing Circles

 

 It's easy to write an equation that has a graph that's a circle. It's:

 

 X2 + Y2 = any positive number

 
 The equation makes a circle as long as the exponents on X and Y are both 2
 and the coefficients on X and Y are both the same (usually 1).
 The "any positive number" on the other side of the equation
 is the radius of the circle times itself (r 2).
 
 The circle, unless we move it, is centered at the (0,0) point.
 
 Example:
 Say we have ...

 X2 + Y2 = 16

 
 which could be written as ...

 X2 + Y2 = 42

 
 This makes a graph that looks like this:
 

 

 
 This is a circle with it's center at the origin (0,0) and a radius of 4.
 
 There are two ways that we can change the circle.
 We can make it bigger or smaller (by changing the number on the right side)
 AND we can move the center of the circle away from (0,0).
 
 To move the center, we add or subtract numbers from the X or Y.
 
 Example:

 

 
 The -2 part next to the X moves the circle two units TO THE RIGHT.
 

 

 
 The -4 part next to the Y moves the circle four units UP.
 

 

 
 The -3 next to the X moves the circle 3 units to the right.
 The +5 next to the Y moves the circle 5 units down.
 
 If the coefficients next to the X and Y are the same but not 1,
 we have some work to do before we can see the center and the radius.
 
 Example:

 

 
 So the center of this circle is at X = 0, Y = 4, 
 and the radius is about 1.414.
 
 About 1.414????
 Isn't it 2?
 
 NOPE!
 
 The number on the right is the radius SQUARED!
 To find the radius, we need the square root of that number.
 
 The square root of 2 is about 1.414.
 
 If the coefficients on the X 2 and the Y 2 terms are not the same,
 or if we have a minus sign on either one,
 we don't have a circle.
 We have something else!
 

   copyright 2005 Bruce Kirkpatrick

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