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Write an equation In standard form for the circle. -4 12 16 x -13 w16- o (x - 6) + (y+ 8)* - 64 %3D o (* + 6) + (y- 8)' - 64 o (t+ 6)* + (y + 8)° = 64 O (*-6) + (y - 8)° - 64

Write an equation In standard form for the circle. -4 12 16 x -13 w16- o (x - 6) + (y+ 8)* - 64 %3D o (* + 6) + (y- 8)' - 64 o (t+ 6)* + (y + 8)° = 64 O (*-6) + (y - 8)° - 64

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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**Topic: Writing the Equation of a Circle in Standard Form** ### Problem: Write an equation in standard form for the circle. ### Diagram Description: The diagram shows a coordinate plane with the circle plotted on it. The x-axis and y-axis are drawn, with both axes labeled for scale. Major points on the axes are marked: - x-axis: ranges from -16 to 16 - y-axis: ranges from -16 to 16 The circle is centered at (x = 6, y = -8) and has a radius of 8 units. ### Answer Choices: Choose the correct standard form equation for the circle from the options below: 1. \( (x - 6)^2 + (y + 8)^2 = 64 \) 2. \( (x + 6)^2 + (y - 8)^2 = 64 \) 3. \( (x + 6)^2 + (y + 8)^2 = 64 \) 4. \( (x - 6)^2 + (y - 8)^2 = 64 \) ### Explanation: To write the equation of a circle in standard form, we use the formula: \[ (x - h)^2 + (y - k)^2 = r^2 \] Where: - \((h, k)\) is the center of the circle. - \(r\) is the radius. **In this case:** - The center of the circle is (6, -8). - The radius given is 8 units, thus \( r^2 = 8^2 = 64 \). By substituting \((h, k)\) and \(r\) into the standard form equation, we obtain: \[ (x - 6)^2 + (y + 8)^2 = 64 \] Thus, the correct answer is option 1: \[ (x - 6)^2 + (y + 8)^2 = 64 \]
Transcribed Image Text:**Topic: Writing the Equation of a Circle in Standard Form** ### Problem: Write an equation in standard form for the circle. ### Diagram Description: The diagram shows a coordinate plane with the circle plotted on it. The x-axis and y-axis are drawn, with both axes labeled for scale. Major points on the axes are marked: - x-axis: ranges from -16 to 16 - y-axis: ranges from -16 to 16 The circle is centered at (x = 6, y = -8) and has a radius of 8 units. ### Answer Choices: Choose the correct standard form equation for the circle from the options below: 1. \( (x - 6)^2 + (y + 8)^2 = 64 \) 2. \( (x + 6)^2 + (y - 8)^2 = 64 \) 3. \( (x + 6)^2 + (y + 8)^2 = 64 \) 4. \( (x - 6)^2 + (y - 8)^2 = 64 \) ### Explanation: To write the equation of a circle in standard form, we use the formula: \[ (x - h)^2 + (y - k)^2 = r^2 \] Where: - \((h, k)\) is the center of the circle. - \(r\) is the radius. **In this case:** - The center of the circle is (6, -8). - The radius given is 8 units, thus \( r^2 = 8^2 = 64 \). By substituting \((h, k)\) and \(r\) into the standard form equation, we obtain: \[ (x - 6)^2 + (y + 8)^2 = 64 \] Thus, the correct answer is option 1: \[ (x - 6)^2 + (y + 8)^2 = 64 \]
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