1. Unit 5: Geometric and Algebraic Connections
5.5 Equations of Circles

2. Trinomial 16 529 144 49 Completing the Square
To complete the square: Take half, then square it! 16
529
144 49

3. (𝒙−𝟑) 𝟐 +( 𝒚−(−𝟐)) 𝟐 = 𝟒 𝟐
(𝒙−𝟑) 𝟐 +( 𝒚+𝟐) 𝟐 =𝟏𝟔
= (𝟏−𝟒 ) 𝟐 +(−𝟏− −𝟏 ) 𝟐
= ( −𝟓) 𝟐 +(𝟎 ) 𝟐
Radius: =𝟓
(𝒙−𝟒) 𝟐 +( 𝒚−(−𝟏)) 𝟐 = 𝟓 𝟐
(𝒙−𝟒) 𝟐 +( 𝒚+𝟏) 𝟐 =𝟐𝟓

4. (𝒙−𝟐) 𝟐 +( 𝒚−(−𝟗)) 𝟐 = 𝟏𝟏 𝟐
(𝒙−𝟐) 𝟐 +( 𝒚+𝟗) 𝟐 =𝟏𝟏
= (−𝟑−𝟐 ) 𝟐 +(𝟏𝟔−𝟒 ) 𝟐
= ( −𝟓) 𝟐 +(𝟏𝟐 ) 𝟐
Radius:
=𝟏𝟑
(𝒙−𝟐) 𝟐 +( 𝒚−𝟒) 𝟐 = 𝟏𝟑 𝟐
(𝒙−𝟐) 𝟐 +( 𝒚−𝟒) 𝟐 =𝟏𝟔𝟗

5. (𝟔, −𝟑) 𝟓 = −𝟔+𝟐 𝟐 , 𝟑𝟐+𝟐𝟔 𝟐 = −𝟐, 𝟐𝟗 (−𝟑, 𝟑) 𝟔 Center: Radius:
= −𝟔+𝟐 𝟐 , 𝟑𝟐+𝟐𝟔 𝟐
= −𝟐, 𝟐𝟗
Center:
(−𝟑, 𝟑)
Radius:
= (−𝟐 −𝟐 ) 𝟐 +(𝟐𝟗−𝟐𝟔 ) 𝟐
Radius: 𝟔
= ( −𝟒) 𝟐 +(𝟑 ) 𝟐 =𝟓

6. (𝟒, −𝟑) 𝟔 = 𝟐+𝟏𝟐 𝟐 , 𝟖+𝟐𝟒 𝟐 = 𝟕, 𝟏𝟔 (𝟓, 𝟓) 𝟒 Center: Radius: Center:
= 𝟐+𝟏𝟐 𝟐 , 𝟖+𝟐𝟒 𝟐
= 𝟕, 𝟏𝟔
Radius:
Center:
(𝟓, 𝟓)
= (𝟕 −𝟐 ) 𝟐 +(𝟏𝟔−𝟖 ) 𝟐
= ( 𝟓) 𝟐 +(𝟖 ) 𝟐
Radius: 𝟒
= 𝟖𝟗

7. Center:
(𝟒, 𝟎)
Center:
(𝟒, −𝟏)
Radius: 𝟑
Radius: 𝟕

8. Center:
(−𝟐, 𝟑)
Center:
(𝟐, 𝟑)
Radius: 𝟒
Radius: 𝟓

9. (−𝟏, −𝟑) 𝟕 𝒙 𝟐 + 𝒚 𝟐 +𝟐𝒙+𝟔𝒚−𝟑𝟗=𝟎 (−𝟓, 𝟔) 𝟐 𝒙 𝟐 + 𝒚 𝟐 +𝟏𝟎𝒙−𝟏𝟐𝒚−𝟓𝟕=𝟎
Center:
(−𝟏, −𝟑)
Radius: 𝟕
𝒙 𝟐 + 𝒚 𝟐 +𝟐𝒙+𝟔𝒚−𝟑𝟗=𝟎
Center:
(−𝟓, 𝟔)
Radius: 𝟐
𝒙 𝟐 + 𝒚 𝟐 +𝟏𝟎𝒙−𝟏𝟐𝒚−𝟓𝟕=𝟎

10. yes
yes

11. no no