Mapping Rules for Equations of the Circle
Our standard equation of the "unit circle" is x2 + y2 = 1.
Whenever we make adjustments to our base circle
(moving it to the left or right, up or down or making it
bigger) we must write a mapping rule for the equation of
the circle to show how our x and y values change.
Mapping Rule #1
Increasing the radius of the circle:
x2 + y2 = r2
(x, y) --> (rx, ry)
Dec 4­1:30 PM
Mapping Rule #2
Moving the Center of the Circle
(x - h)2 + (y - k)2 = 1
(x, y) --> (x + h, y + k)
Note: The mapping rule and
the coordinates are always
the same, the equation is
different...
C(2, ­1) r = 1
Dec 10­8:48 PM
What is the mapping notation?
(0, 1)
(1, 0)
(-1, 0)
(0, -1)
Dec 18­7:20 PM
Example:
What is the mapping notation for the following questions?
1 = (x + 3)2 + (y - 4)2
1 = (x - 4)2 + (y + 2)2
1 = (x + 2)2 + (y - 1)2
1 = (x - 18)2 + (y + 2)2
Dec 9­11:57 AM
Putting them both together....
Example:
What is the mapping notation for the following questions?
16 = (x + 3)2 + (y - 4)2
36 = (x - 4)2 + (y + 2)2
25 = (x + 2)2 + (y - 1)2
14 = (x - 18)2 + (y + 2)2
Dec 10­8:50 PM
Remember FOIL?
(x-3)(x-3)
(2x-2)(2x-2)
Nov 6­3:42 PM
(3x+2)(3x+2)
General Form of the Equation
You are frequently given the equation of a circle in standard form and may
need to change it to general form.
Ax2 + Ay2 + Bx + Cy + D= 0
**MUST BE IN THIS FORMAT!!!!
2x2 + 2y2 + 4x + 3y + 2= 0
Example:
(standard form)
4 = (x + 3)2 + (y - 1)2
4 = (x + 3)(x + 3) + (y - 1)(y - 1)
4 = x2 + 3x + 3x + 9 + y2 - y - y + 1
4 = x2 + 6x + 9 + y2 - 2y + 1
4 = x2 + y2 + 6x - 2y + 10
0 = x2 + y2 + 6x - 2y + 6
(general form)
Dec 14­10:46 AM
Nov 7­10:41 AM
Nov 6­3:23 PM