Solve the Problem $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$

question 126

Multiple Choice

Solve the problem.
-Recall that an equation of a circle can be written in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ , where $( h , k )$ is the center and $r$ is the radius. Expanding terms, the equation can also be written in the form $x ^ { 2 } + y ^ { 2 }$ $+ A x + B y + C = 0$ .
a . Find an equation of the form $x ^ { 2 } + y ^ { 2 } + A x + B y + C = 0$ that represents the circle that passes through the three points $( 4 , - 4 ) , ( 2 , - 8 )$ , and $( - 5 , - 1 )$ .
b. Find the center and radius of the circle.

• A) a. \(x ^ { 2 } + y ^ { 2 } - 2 x - 8 y - 8 = 0\)
• b. Center: \(( 1,4 )\); Radius: 4
• B) a. \(x ^ { 2 } + y ^ { 2 } - 2 x - 8 y - 8 = 0\)
• b. Center: \(( - 1 , - 4 )\); Radius: 5
• C) a. \(x ^ { 2 } + y ^ { 2 } + 2 x + 8 y - 8 = 0\)
• b. Center: \(( 1,4 )\); Radius: 4
• D) a. \(x ^ { 2 } + y ^ { 2 } + 2 x + 8 y - 8 = 0\)
• b. Center: \(( - 1 , - 4 )\); Radius: 5

Identify and differentiate between various economic systems and their characteristics.

Recognize the role and impact of government intervention in economic systems.

Understand the concept of full-cost pricing and its implications on markets and environmental policies.

Grasp the principles of market systems, including demand, supply, and market equilibrium.

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Definitions:

Conflict Theory

A sociological perspective that views social life as competition, focusing on the distribution of resources, power, and inequality within a society.

Oppressive Force

A power or influence that limits freedom or development, often manifesting through social, political, or economic means.

Liberating Force

An entity or movement that aims to free individuals or societies from oppression, restrictions, or tyranny, promoting freedom and independence.

Power Elite

A term used in political and sociological theory to describe a small group of powerful people who hold a disproportionate amount of wealth, privilege, political power, or skill in a society.