Find the Equation of the Circle $$x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$$

question 1

Multiple Choice

Find the equation of the circle
$$x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$$
that passes through the points $( 1,9 ) , ( - 4,4 ) , ( 6,4 )$ .

• A) \(x ^ { 2 } + y ^ { 2 } - 2 x - 8 y - 8 = 0\)
• B) \(x ^ { 2 } + y ^ { 2 } - x - 4 y - 8 = 0\)
• C) \(x ^ { 2 } + y ^ { 2 } - 2 x - 8 y + 42 = 0\)
• D) \(x ^ { 2 } + y ^ { 2 } - 2 x - 8 y - 25 = 0\)
• E) \(x ^ { 2 } + y ^ { 2 } - x - 4 y - 25 = 0\)

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Definitions:

Functional Designs

Designs that prioritize the practicality and function of a product, facility, or system over aesthetic considerations.

Economical

Economical pertains to the efficient and judicious use of resources, often with the aim of minimizing cost and waste while achieving a specific purpose or outcome.

Simple Design

The creation of a product or solution that is straightforward, easy to use, and free of unnecessary complexity.

Network Organization Design

A flexible approach to structuring an organization where coordination is achieved through informal networks and relationships rather than through a formal hierarchical structure.