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

question 13

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:

Unjust Favoritism

A situation where preferential treatment is given without fair standards or merit, often leading to dissatisfaction and conflict within groups.

Group Harmony

The state of agreement and cooperation among members of a group, achieved by minimizing conflicts and emphasizing common interests.

Individualism

A theoretical approach that prioritizes individual autonomy over the power of groups or governmental authority.

Collectivism

A cultural or societal approach that prioritizes the group's needs and goals over individual desires or ambitions.