Complete the Square and Write the Equation in Standard Form $$x ^ { 2 } + y ^ { 2 } - 18 x + 2 y + 82 = 4$$

question 80

Multiple Choice

Complete the square and write the equation in standard form. Then give the center and radius of the circle.
- $$x ^ { 2 } + y ^ { 2 } - 18 x + 2 y + 82 = 4$$

• A) \(( x - 9 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 4\)
• \(( 9 , - 1 ) , r = 2\)
• B) \(( x + 1 ) ^ { 2 } + ( y - 9 ) ^ { 2 } = 4\)
• \(( - 1,9 ) , r = 2\)
• C) \(( x - 9 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 4\)
• \(( - 9,1 ) , r = 4\)
• D) \(( x + 1 ) ^ { 2 } + ( y - 9 ) ^ { 2 } = 4\)
• \(( 1 , - 9 ) , \mathrm { r } = 4\)

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Definitions:

Optimizing

Optimizing involves making the best or most effective use of a situation or resource, often by balancing different factors or constraints.

Herbert Simon

An American economist, political scientist, and cognitive psychologist known for his contributions to decision-making processes and artificial intelligence.

Satisfactory Alternatives

Acceptable options or solutions that are considered adequate for meeting a particular need or solving a problem, albeit not necessarily the best possible ones.

Optimal Decisions

The process of choosing the best possible solution or course of action from among various alternatives based on specific criteria and objectives.