coordinate point for a circle
standard form equation of a circle
r squared = (x-h) squared + (y-k) squared
standard form of an equation of a circle if the center of the circle is the origin
x squared + y squared = r squared
standard form of an equation of a circle if the center is a unit circle
x squared + y squared = 1
general form of an equation of a circle
x squared + y squared + Dx + Ey = -F
further expanded general form of an equation of a circle
x squared + Dx + (D/2) squared + y squared + Ey + (E/2) squared = -F + (D/2) squared + (E/2) squared
How do you complete the square?
take half the middle term's coefficient, square it, and add that to both sides
How do you plot a circle?
Plot the center, and count out the distance of the circle's radius directly above, below, left, and right of the point.
How do you find the equation of a circle given three points
Plug in each coordinate pair into the general form. Then use a matrix to solve for D, E, and F. Then plug those variables back in to a blank general form (leaving x and y in variable form.)
How do you transfer an equation to standard form from general form and visa versa?
Complete the square and simplify.