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Select the appropriate graph for the circle in Euclidean geometry: (x+3)^2+(y-2)

Select the appropriate graph for the circle in Euclidean geometry: (x+3)^2+(y-2)

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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Select the appropriate graph for the circle in Euclidean geometry: (x+3)^2+(y-2)^2=16.

The image contains two graphs, labeled c. and d., depicting circles on a coordinate grid. Graph c: - The circle is centered at the point (3, 3) on the coordinate plane. - The radius of the circle extends to approximately 6 units vertically and horizontally, touching the y-axis at 0 and 6, and the x-axis at 6 and 0. - The grid indicates both the x and y-axes marked in increments of 1. Graph d: - The circle is centered at the origin, (0, 0), of the coordinate plane. - The radius appears to be approximately 6 units, as indicated by the circle touching the x and y-axes at 6 and -6. - The grid shows the x and y-axes marked in increments of 1. Both graphs are labeled sequentially with "Choice 3" and presented on a standard Cartesian coordinate system with grids to aid in precise measurement and analysis of the circle's position and dimensions.
Transcribed Image Text:The image contains two graphs, labeled c. and d., depicting circles on a coordinate grid. Graph c: - The circle is centered at the point (3, 3) on the coordinate plane. - The radius of the circle extends to approximately 6 units vertically and horizontally, touching the y-axis at 0 and 6, and the x-axis at 6 and 0. - The grid indicates both the x and y-axes marked in increments of 1. Graph d: - The circle is centered at the origin, (0, 0), of the coordinate plane. - The radius appears to be approximately 6 units, as indicated by the circle touching the x and y-axes at 6 and -6. - The grid shows the x and y-axes marked in increments of 1. Both graphs are labeled sequentially with "Choice 3" and presented on a standard Cartesian coordinate system with grids to aid in precise measurement and analysis of the circle's position and dimensions.
### Transcription for Educational Website #### Graphs and Description: **Graph a.** - This graph shows a circle centered at approximately (3, -3) on a Cartesian plane. - The circle appears to have a radius of about 5 units. - The horizontal axis ranges from -12 to 12, and the vertical axis ranges from -8 to 8. - The circle intersects the x-axis near x = 8 and x = -2, and the y-axis near y = 2 and y = -8. - Labeled as "Choice 4." **Graph b.** - This graph displays a circle centered at approximately (-4, 1) on a Cartesian plane. - Similar to Graph a, this circle also appears to have a radius of about 5 units. - The horizontal axis ranges from -12 to 12, and the vertical axis ranges from -8 to 8. - The circle intersects the x-axis near x = -9 and x = 1, and the y-axis near y = 6 and y = -4. - Labeled as "Choice b." Each circle is plotted with a thin green line on a grid, which is helpful for visualizing the position and dimensions accurately within the defined boundaries.
Transcribed Image Text:### Transcription for Educational Website #### Graphs and Description: **Graph a.** - This graph shows a circle centered at approximately (3, -3) on a Cartesian plane. - The circle appears to have a radius of about 5 units. - The horizontal axis ranges from -12 to 12, and the vertical axis ranges from -8 to 8. - The circle intersects the x-axis near x = 8 and x = -2, and the y-axis near y = 2 and y = -8. - Labeled as "Choice 4." **Graph b.** - This graph displays a circle centered at approximately (-4, 1) on a Cartesian plane. - Similar to Graph a, this circle also appears to have a radius of about 5 units. - The horizontal axis ranges from -12 to 12, and the vertical axis ranges from -8 to 8. - The circle intersects the x-axis near x = -9 and x = 1, and the y-axis near y = 6 and y = -4. - Labeled as "Choice b." Each circle is plotted with a thin green line on a grid, which is helpful for visualizing the position and dimensions accurately within the defined boundaries.
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