Write the Equation in Standard Form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$

question 14

Multiple Choice

Write the equation in standard form: $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Then, if possible, identify the center and radius of the circle. If the equation represents a degenerate case, give the solution set.
- $$x ^ { 2 } + y ^ { 2 } + 4 x + 8 y + 11 = 0$$

• A) \(( x + 2 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 9\); Center: \(( - 2 , - 4 )\); Radius: 3
• B) \(( x + 2 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 0 ;\) Degenerate case (single point \() : \{ ( - 2 , - 4 ) \}\)
• C) \(( x + 2 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 9\); Center: \(( 2,4 )\); Radius: 3
• D) \(( x + 2 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = - 9\); Degenerate case: \{ \}

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