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9 Graph the circle with the equation (x + 4)² + (y – 5)² = 9 CIRCLE -10 -9 -8 -7 -6 -5 -4 -3 -2 10 9 D 8 co h 7 6 5 4 3 2 1 -10 N -3 4567 -4 -5 -6 -7 O 1 2 3 4 5 6 7 8 9 10

9 Graph the circle with the equation (x + 4)² + (y – 5)² = 9 CIRCLE -10 -9 -8 -7 -6 -5 -4 -3 -2 10 9 D 8 co h 7 6 5 4 3 2 1 -10 N -3 4567 -4 -5 -6 -7 O 1 2 3 4 5 6 7 8 9 10

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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**Graphing a Circle from an Equation** **Objective:** Graph the circle with the equation \((x + 4)^2 + (y - 5)^2 = 9\). **Equation Analysis:** This equation is in the standard form \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is the radius. - **Center (h, k):** \((-4, 5)\) - **Radius (r):** \(3\) (since the equation equals \(9\) and \(r^2 = 9\)) **Graph Details:** 1. **Axes:** - The graph has a standard Cartesian coordinate system with both x and y axes ranging from \(-10\) to \(10\). 2. **Center Point:** - The point labeled \(A\) at \((-4, 5)\) marks the center of the circle. 3. **Instructions:** - To graph the circle, use the center at \((-4, 5)\). From this center, measure a distance of \(3\) units in all directions (up, down, left, right) to plot points on the circle's circumference. This visualization helps in understanding how the equation of a circle translates to its graphical representation on a coordinate plane.
Transcribed Image Text:**Graphing a Circle from an Equation** **Objective:** Graph the circle with the equation \((x + 4)^2 + (y - 5)^2 = 9\). **Equation Analysis:** This equation is in the standard form \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is the radius. - **Center (h, k):** \((-4, 5)\) - **Radius (r):** \(3\) (since the equation equals \(9\) and \(r^2 = 9\)) **Graph Details:** 1. **Axes:** - The graph has a standard Cartesian coordinate system with both x and y axes ranging from \(-10\) to \(10\). 2. **Center Point:** - The point labeled \(A\) at \((-4, 5)\) marks the center of the circle. 3. **Instructions:** - To graph the circle, use the center at \((-4, 5)\). From this center, measure a distance of \(3\) units in all directions (up, down, left, right) to plot points on the circle's circumference. This visualization helps in understanding how the equation of a circle translates to its graphical representation on a coordinate plane.
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