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The equation of a circle is (x − 10)² + (y − 8)² = 256 . What is the center of the circle? Enter your answer in the boxes.

The equation of a circle is (x − 10)² + (y − 8)² = 256 . What is the center of the circle? Enter your answer in the boxes.

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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Question
**Understanding the Equation of a Circle** The standard form of the equation of a circle is \((x - h)^2 + (y - k)^2 = r^2\), where: - \((h, k)\) is the center of the circle. - \(r\) is the radius of the circle. ### Example Problem Consider the following equation of a circle: \[ (x - 10)^2 + (y - 8)^2 = 256 \] **Question:** What is the center of the circle? **Solution:** To determine the center of the circle, we compare the given equation with the standard form \((x - h)^2 + (y - k)^2 = r^2\). From the given equation: - \(h = 10\) - \(k = 8\) Therefore, the center of the circle is \((10, 8)\). **Answer:** Enter your answer in the boxes provided: [10] [8]
Transcribed Image Text:**Understanding the Equation of a Circle** The standard form of the equation of a circle is \((x - h)^2 + (y - k)^2 = r^2\), where: - \((h, k)\) is the center of the circle. - \(r\) is the radius of the circle. ### Example Problem Consider the following equation of a circle: \[ (x - 10)^2 + (y - 8)^2 = 256 \] **Question:** What is the center of the circle? **Solution:** To determine the center of the circle, we compare the given equation with the standard form \((x - h)^2 + (y - k)^2 = r^2\). From the given equation: - \(h = 10\) - \(k = 8\) Therefore, the center of the circle is \((10, 8)\). **Answer:** Enter your answer in the boxes provided: [10] [8]
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