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

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Definitions:

Discrimination

Unjust or prejudicial treatment of different categories of people, especially on the grounds of race, age, sex, or disability.

Implicit Association Test

A psychological test designed to measure the strength of a person's automatic associations between mental representations of objects in memory.

Stereotypes

Widely held but fixed and oversimplified images or ideas of a particular type of person or thing.

Social Loafing

The tendency for individuals to exert less effort on a task when working in a group than when working alone.