Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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**Determine the equation of the circle graphed below.**

**Graph Description:**

The graph shows a circle plotted on a Cartesian coordinate system with the x-axis ranging from -10 to 10 and the y-axis also ranging from -10 to 10. The circle is centered at the origin (0, -6) and has a radius of 4. The grid lines help verify the circle's dimensions. The circle intersects the y-axis at -2 and -10, confirming its radius.

**Steps to Determine the Equation:**

1. **Identify the Center:** The center of the circle is at (0, -6).
2. **Determine the Radius:** The radius is 4, as it spans 4 units from the center to the edge in all directions.
3. **Write the Equation:** The general form of a circle's equation is \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius. Substituting the known values, the equation becomes:
   \[
   (x - 0)^2 + (y + 6)^2 = 4^2
   \]
   Simplified, this is:
   \[
   x^2 + (y + 6)^2 = 16
   \]

This equation represents the circle shown on the graph.
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Transcribed Image Text:**Determine the equation of the circle graphed below.** **Graph Description:** The graph shows a circle plotted on a Cartesian coordinate system with the x-axis ranging from -10 to 10 and the y-axis also ranging from -10 to 10. The circle is centered at the origin (0, -6) and has a radius of 4. The grid lines help verify the circle's dimensions. The circle intersects the y-axis at -2 and -10, confirming its radius. **Steps to Determine the Equation:** 1. **Identify the Center:** The center of the circle is at (0, -6). 2. **Determine the Radius:** The radius is 4, as it spans 4 units from the center to the edge in all directions. 3. **Write the Equation:** The general form of a circle's equation is \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius. Substituting the known values, the equation becomes: \[ (x - 0)^2 + (y + 6)^2 = 4^2 \] Simplified, this is: \[ x^2 + (y + 6)^2 = 16 \] This equation represents the circle shown on the graph.
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