Find the Center (H, K) and Radius R of the Circle

question 128

Multiple Choice

Find the center (h, k) and radius r of the circle with the given equation.
- $$x ^ { 2 } + y ^ { 2 } - 4 x + 8 y = 29$$

• A) \(( \mathrm { h } , \mathrm { k } ) = ( 4 , - 2 ) ; \mathrm { r } = 49\)
• B) \(( \mathrm { h } , \mathrm { k } ) = ( 2 , - 4 ) ; \mathrm { r } = 7\)
• C) \(( \mathrm { h } , \mathrm { k } ) = ( - 2,4 ) ; \mathrm { r } = 49\)
• D) \(( \mathrm { h } , \mathrm { k } ) = ( - 4,2 ) ; \mathrm { r } = 7\)

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Definitions:

Unconscious Processing

Mental processes that occur without conscious awareness or intention, influencing perceptions, thoughts, and behaviors.

Confirmation Bias

The tendency to search for, interpret, and remember information in a way that confirms one's preconceptions, leading to statistical errors.

System I

A term often used to describe intuitive, fast, and automatic thinking processes, as opposed to more deliberate and analytical decision-making.

System II

A term often used to describe slow, deliberate, and analytical thought processes in dual-process theories of cognition.