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Write standard equation and center and radius for all 7 circles

Write standard equation and center and radius for all 7 circles

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Write standard equation and center and radius for all 7 circles

### Polar Coordinate System Graph The image provided is a graph on a Cartesian coordinate system with a detailed arrangement of multiple circles. #### Description: 1. **Coordinate System**: - The graph is set on a Cartesian coordinate system, featuring both the X-axis (horizontal) and Y-axis (vertical), ranging from -14 to 14 on the X-axis and -18 to 18 on the Y-axis. 2. **Central Circles**: - There are three concentric circles centered at the origin (0,0). - The smallest circle has a radius of approximately 3 units. - The middle circle has a radius of approximately 5 units. - The largest circle has a radius of approximately 7 units. 3. **Outer Circles**: - Four additional circles are located around the largest central circle. - The centers of these outer circles are positioned at: - (0, 7) - (0, -7) - (-7, 0) - (7, 0) - Each of these circles has a radius of approximately 3 units. #### Observations: - The graph shows symmetry along both the X and Y axes. - The arrangement of the circles resembles a geometric pattern often seen in certain types of artistic designs and can serve as a practical example in understanding symmetry and coordinate systems. This graph is a useful example for educational purposes, illustrating the relationships between geometric shapes in a coordinate plane, and providing a basis for learning about Cartesian coordinates, symmetry, and circle equations.
Transcribed Image Text:### Polar Coordinate System Graph The image provided is a graph on a Cartesian coordinate system with a detailed arrangement of multiple circles. #### Description: 1. **Coordinate System**: - The graph is set on a Cartesian coordinate system, featuring both the X-axis (horizontal) and Y-axis (vertical), ranging from -14 to 14 on the X-axis and -18 to 18 on the Y-axis. 2. **Central Circles**: - There are three concentric circles centered at the origin (0,0). - The smallest circle has a radius of approximately 3 units. - The middle circle has a radius of approximately 5 units. - The largest circle has a radius of approximately 7 units. 3. **Outer Circles**: - Four additional circles are located around the largest central circle. - The centers of these outer circles are positioned at: - (0, 7) - (0, -7) - (-7, 0) - (7, 0) - Each of these circles has a radius of approximately 3 units. #### Observations: - The graph shows symmetry along both the X and Y axes. - The arrangement of the circles resembles a geometric pattern often seen in certain types of artistic designs and can serve as a practical example in understanding symmetry and coordinate systems. This graph is a useful example for educational purposes, illustrating the relationships between geometric shapes in a coordinate plane, and providing a basis for learning about Cartesian coordinates, symmetry, and circle equations.
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