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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Definitions:

Factorial Designs

Experimental designs used in research that involve multiple factors (independent variables) and their influence on the dependent variable, allowing for the study of interactions among factors.

Experimental Studies

Research methods that involve the manipulation of variables to determine cause-and-effect relationships.

Variables

Elements or factors that can change and potentially affect the outcome of a study or experiment.

Hypothesis

A suggested interpretation put forward with scarce evidence, serving as an initial step for more in-depth exploration.