CIRCLES

As always I will be taking advantage of the “post about whatever you want on holidays” rule. This week I’m going to talk about, drum roll please, CIRCLES!!!!!!
The standard form of a circle is (x-h)^2 + (y-k)^2 =r^2. (h,k) is the center and r is the radius.
To find the radius you can use the distance formula with the center and point on the outside or you can half the diameter found by using two points on the outside through the center.

To find the equation of a circle you must put it in standard form by completing the square.

1. Divide by leading coff., then move all numbers to the right

2. Half the middle term then square it and add both sides

3. Factor

When you graph in your calculator you need to slove for y and put a positive and negative formula in for y equals.

When you find the intersection of a line and circle
- solve the line for y
- plug circle equation for y
- slove th equadractic
- if you get i they DO NOT INTERSECT
(Please excuse my horrible note taking, I tend to be an idiot at the beginning of the school year and these notes are from August.)

EXAAAAAMPLEEEEEE TIIIIIIIIIIME
x^2 - 4x + y^2 + 6y + 4 = 0

subtract 4 from both sides (step one)
x^2 - 4x + y^2 + 6y = -4

half the middle term then square and add to both sides.
-4/2=(-2) ^2=4
6/2=3 ^2=9

x^2 - 4x + 4 + y^2 + 6y + 9 = -4 + 4 + 9

Factor
(x-2)^2 + (y+3)^2 = 9

Your center is (2,-3) and your radius is 3
THAT IS HOW YOU DO IT
See you guys tomorrow :/
--Sarah(: