Section 6.2 – The Circle

2 2 2x y rh k

h, kCenter : Radius : r

Write the standard form of each equation. Then graph the equation. 2 2 2x y rh k

h, kCenter : Radius : r

center (0, 3) and radius 2

h = 0, k = 3, r = 2

2 2 2x y 20 3

22x y 3 4

Write the standard form of each equation. Then graph the equation. 2 2 2x y rh k

h, kCenter : Radius : r

center (-1, -5) and radius 3

h = -1, k = -5, r = 3

2 2 231 5x y

2 2x 1 y 5 9

Write the standard form of each equation. Then graph the equation. 2 2 2x y rh k

h, kCenter : Radius : r

2 2x y 4x 9

22x 4x y 9

22 4 4x 4x y 9

22 2x y 32 1

2 2x 2 y 13

-2, Center: Radius0 : 13

Write the standard form of each equation. Then graph the equation. 2 2 2x y rh k

h, kCenter : Radius : r

2 2x y 6y 50 14x

2 2x 14x y 6y 50

2 2x 14x y 6y 5049 9 49 9

22 2 108y7x 3

2 2x 7 y 3 108

-7, -Center: Radius:3 108

Write the standard form of each equation. Then graph the equation. 2 2 2x y rh k

h, kCenter : Radius : r

2 2x y 18x 18y 53 0

2 2x 18x y 18y 53

2 2x 18x y 1881 81 81 8y 3 15

22 29 9 1 9x 0y

2 2x 9 y 9 109

9, 9Center: Radius: 109

2 24x 4y 36x 5 0

2 24x 36x 4y 5

2 24 x 9x 4 y 5

2 2x 9x 481 814 44 4

y 5

2

294 x 4 y 762

2

294 x 4 y 762

4 4 4

2

2292

x y 19

-9 , 1Center: Radius: 9 02

2 23x 3y 6x 1

2 23x 6x 3y 1

2 23 x 2x 3 y 1

22x 2x 3 y 1 33 1

2 23 x 1 3 y 4

2

2 2 4x 1 y3

-1, Center: Radius0 : 4

3

2 23 x 1 3 y 43 3 3

2 22x 2y 28x 12y 114 0

2 22x 28x 2y 12y 114

2 22 x 14x 2 y 6y 114

2 2x 14x y 6y2 49 2 9 911 184 8

2 22 x 7 2 y 3 2

7, -Center: Radius3 : 1

2 2x y7 3 1

Find the equation of the circle with center (8, -9) and passes through the point (21, 22).

2 2 2x y rh k

2 2 2x 8 y 9 r

2 2 221 8 22 9 r 21130 r

2 2x 8 y 9 1130

Find the equation of the circle with center (-13, 42) and passes through the origin

2 2 2x y rh k

2 2 2x 13 y 42 r

2 2 20 13 0 42 r 21933 r

2 2x 13 y 42 1933

Find the equation of the circle whose endpoints of a diameterare (11, 18) and (-13, -20)

Center is the midpoint of the diameter

11 13 18 20, 1 1,2 2

Radius uses distance formula

2 21 2 1 2r x x y y

2 2r 11 1 18 1

r 505

2 2r 13 1 20 1

r 505

22 21 1 05x 5y