



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






X^{2}
+ Y^{2} = 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 ... 


X^{2}
+ Y^{2} = 16






which
could be written as ... 


X^{2}
+ Y^{2} = 4^{2}






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 
