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

question 29

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.
- $$x ^ { 2 } + y ^ { 2 } - 4 x + 2 y + 5 = 0$$

• A) \(( x - 2 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 25\); Center: \(( - 2,1 )\); Radius: 5
• B) \(( x - 2 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 25\); Center: \(( 2 , - 1 )\); Radius: 5
• C) \(( x - 2 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 0\); Degenerate case (single point): \(\{ ( 2 , - 1 ) \}\)
• D) \(( x - 2 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = - 5\); Degenerate case: \{ \}

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