(x +4)^{2} + (y – 12)^{2}= 36 is the standard equation of a circle whose center is (-4, 12 ) and radius is 6. NOTICE the **opposite** values of the center are used in the equation. Also, for the equation the radius, r, is squared.

** Graph the center (-4, 12). Do you recall that is in the 2nd quadrant? **

**Then graph 4 points by starting at the center each time**. Go up 6 for the first point. Again from the center go down 6. Repeat two more times: go left and then also right.

**Draw the circle through the 4 points.** ** Test one of your 4 points. What do I mean? ** If a point is on the

**circle**then it will make the equation TRUE. If you started at (-4,12) and went up 6 then you should have the point (-4, 18). Now use x= – 4 and y=18 in the equation, will it make a TRUE math expression? You will have only numbers so it should be easy to decide as long as you recall the Order of Operations.

(x +4)^{2} + (y – 12)^{2}** = 36 ** Let x= – 4 and y=18 and we get

(-4 +4)^{2} + (18 – 12)^{2} = **36**. We will get 0 + 36 = **36**. This is true so we know the point (-4, 18) is correct. I will let you test the other 3 points that you found.