Unit 5: Geometric and Algebraic Connections 5.5 Equations of Circles

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

(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

(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

(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

(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

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

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

(−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

yes yes

no no