Circles
Non-Standard Form
Example
Graph 2x2 + 2y2 - 12x + 28y - 12 = 0.
Step 1 . Identify the conic section.
This is a circle because the x and y terms are both squared,
have the same coefficient, and are added.
Step 2 . Write equation in standard form.
x 2 + y2 - 6x + 14y - 6 = 0; divide by the coefficient 2
(x2-6x) + (y2+14y) = 6; Group the x terms, group the y terms, and move the constant
(x2 - 6x + 9) + (y2 + 14y + 49) = 6 + 9 + 49; complete the square for x and y
(x - 3)2 + (y + 7)2 = 64; Simplify
Step 3. Graph the conic.
Identify the center (3, -7)
Identify the radius r = 8
