1. Chapter 9 Section 8:
Equations of Circles

2. Remember the distance formula? Distance =
Use the distance formula to find the radius of the circle.
**Remember, you can also make a right triangle on the coordinate plane and use Pythagorean Theorem!
Once we find the radius, we can use it and the center to find the equation of a circle:
Standard Equation of a Circle: _______________
where (h,k) is the _________ and r is the ________.
The equation of the Circle C with center (-1,4) is: _______________
Radius= 5 2 2 2
(x – h) + (y – k) = r
center
radius 2 2
(x + 1) + (y – 4) = 25

3. with center C(-3, 6) and a y = (x + 2) + (y – 3) = 10
Examples:
Write an equation for a circle Graph the circle whose equation is
with center C(-3, 6) and a y = (x + 2) + (y – 3) = 10
radius of 6 units. Graph it. 2 2 2 2
(x + 3) + (y – 6) = 36
Center: (-2, 3) Radius: 3.16

4. Determine the coordinates of the center and the measure
of the radius for each circle whose equation is given.
center: _______ center: _________ center: ________ radius: _______ radius: _________ radius: _________
(3/4, -3)
(-4, 0)
(0, 0)
9/2 or 4.5 11
2.83
Write an equation of Circle P based on the given information.
6. Center: P(0,0); Center: P(-1, 4); radius radius: radius:
8. Center: P(0,- ) 5 2 2 2 2 2
x y = 25
(x + 1) + (y – 4) = 15 2
x + (y + 1.5) = 16/9

5. That's all!
Assignment: Equation of circles ws