1. All about circle

2. r (x, y) A circle is a set of points in the xy-plane that are a fixed
distance r from a fixed point (h,k).
The fixed distance is called the radius, and the fixed
point (h,k) is called the center of the circle. x y
(x, y) r
Center:(h, k)

3. The standard form of an equation of a circle with radius r and center (h,k) is

4. ( ) x y + − = 1 3 16 2
Graph ⧭ x y ⧭ ⧳ ⧭ ⧭

5. Find the Equation of the Circle
(-1,3)
(3,3)
(-1, 7)
(-5, 3)
(-1, -1) x y
(x+1)2+(y-3)2=16

6. The general form of the equation of a circle

7. Find the center and the radius of
First group terms:

8. Add appropriate terms to complete the squares for x and for y.

9. (x+5)2 + y 2 = 17 Distance Formula:
Writing the equation of a circle given its center and a point on the circle
The point(-6,4)lies on a circle whose center is at (-5,0)               .
Find the equation of this circle.
Distance Formula:
The distance between the points P and Q is
(x+5)2 + y 2 = 17

10. Writing the equation of a circle given the endpoints of a diameter
Find the equation of the circle whose diameter has endpoints (2,3) and (-2,-5)               .
x2 + (y-1) 2 = 29

11. Classwork 1. (0,0), 10 2. (-4,-6), 7 3. (2,3), 4.5 4. (-6,10), 1
Write the Equation of the circle with the given center and radius:
1. (0,0), 10
2. (-4,-6), 7
3. (2,3), 4.5
4. (-6,10), 1
Graph and find the center and radius of the following circle
1. x2 + y2 =4
2. x2 + (y+1)2 =9
3. (x+5)2 + y2 =81
4. (x+2)2 + (y+4)2 =25