Activity: Search the Logo! Determine the center and the radius of the circle that is defined by each of the following equations.
The circle on a single coordinate plane to reveal the logo.
Color each graph according to its equation. 1. (X + 5)² + y² = 2²; graph: Blue 2. X² + Y² -4 = 0; graph: Black 3. (X - 5)² + y² = 4; graph: Red 4. (X+3)² + (Y + 2)² = 2²; graph: Yellow 5. x² + y² - 6x + 4y - 4 = 0; graph: Green
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The circle on a single coordinate plane to reveal the logo.
Color each graph according to its equation. 1. (X + 5)² + y² = 2²; graph: Blue 2. X² + Y² -4 = 0; graph: Black 3. (X - 5)² + y² = 4; graph: Red 4. (X+3)² + (Y + 2)² = 2²; graph: Yellow 5. x² + y² - 6x + 4y - 4 = 0; graph: Green
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Answer:
To determine the center and radius of each circle, we need to write each equation in standard form:
1. (X + 5)² + y² = 2²
Standard form: (x - (-5))² + (y - 0)² = 2²
Center: (-5, 0)
Radius: 2
Graph: Blue
2. X² + Y² -4 = 0
Standard form: (x - 0)² + (y - 0)² = 2²
Center: (0, 0)
Radius: 2
Graph: Black
3. (X - 5)² + y² = 4
Standard form: (x - 5)² + (y - 0)² = 2²
Center: (5, 0)
Radius: 2
Graph: Red
4. (X+3)² + (Y + 2)² = 2²
Standard form: (x - (-3))² + (y - (-2))² = 2²
Center: (-3, -2)
Radius: 2
Graph: Yellow
5. x² + y² - 6x + 4y - 4 = 0
Standard form: (x - 3)² + (y + 2)² = 3²
Center: (3, -2)
Radius: 3
Graph: Green
To reveal the logo, we need to superimpose the graphs on a single coordinate plane. We can see that the five circles form the logo of the Olympic Games, with each circle representing one of the five continents (Africa, the Americas, Asia, Europe, and Oceania).