6-2 Circles

Dear BRob, this is Danielle Sharp from 1st hour. I never got your e-mail, and i thought that I could use someone else's link but it didn't work, so I'm posting in Sarah's blog cause she's at my house and she let me on it. Anyway, here it goes.

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 need to 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

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

subtract 4 from both sides (step 1)
x^2 - 4x + y^2 + 6y = -4

(step 2) half the middle term then square and add to both sides.
-4 dvided by 2 equals (-2) then square that and it equals 4
6 divided by 2 equals 3 then square that adn it equals 9
x^2 - 4x + 4 + y^2 + 6y + 9 = -4 + 4 + 9

(step 3) factor
(x-2)^2 + (y+3)^2 = 9
*If you have trouble factoring the equation will always lead back to the number after dividing but before squaring

Your center is (2,-3) and your radius is 3

And that is how you slove for a circle, hope you enjoyed :)
-- Danielle Sharp!