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**Circle Equation Problem** **Objective**: Find the standard form of the equation of a circle with the following properties: - **Center**: \((-9, -7)\) - **Tangent to the x-axis** **Task**: Type the standard form of the equation of this circle. *(Type your equation in the provided answer box.)* --- **Explanation**: For a circle tangent to the x-axis, the vertical distance from the center to the x-axis is equal to the radius. Since the center is at \((-9, -7)\), and the y-coordinate is \(-7\), the radius is \(7\). 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 and \( r \) is the radius. For this problem, \( h = -9 \), \( k = -7 \), and \( r = 7 \). Thus, the standard form of the circle's equation is: \[ (x + 9)^2 + (y + 7)^2 = 49 \]

**Circle Equation Problem** **Objective**: Find the standard form of the equation of a circle with the following properties: - **Center**: \((-9, -7)\) - **Tangent to the x-axis** **Task**: Type the standard form of the equation of this circle. *(Type your equation in the provided answer box.)* --- **Explanation**: For a circle tangent to the x-axis, the vertical distance from the center to the x-axis is equal to the radius. Since the center is at \((-9, -7)\), and the y-coordinate is \(-7\), the radius is \(7\). 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 and \( r \) is the radius. For this problem, \( h = -9 \), \( k = -7 \), and \( r = 7 \). Thus, the standard form of the circle's equation is: \[ (x + 9)^2 + (y + 7)^2 = 49 \]

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Circle Equation Problem** **Objective**: Find the standard form of the equation of a circle with the following properties: - **Center**: \((-9, -7)\) - **Tangent to the x-axis** **Task**: Type the standard form of the equation of this circle. *(Type your equation in the provided answer box.)* --- **Explanation**: For a circle tangent to the x-axis, the vertical distance from the center to the x-axis is equal to the radius. Since the center is at \((-9, -7)\), and the y-coordinate is \(-7\), the radius is \(7\). 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 and \( r \) is the radius. For this problem, \( h = -9 \), \( k = -7 \), and \( r = 7 \). Thus, the standard form of the circle's equation is: \[ (x + 9)^2 + (y + 7)^2 = 49 \]
Transcribed Image Text:**Circle Equation Problem** **Objective**: Find the standard form of the equation of a circle with the following properties: - **Center**: \((-9, -7)\) - **Tangent to the x-axis** **Task**: Type the standard form of the equation of this circle. *(Type your equation in the provided answer box.)* --- **Explanation**: For a circle tangent to the x-axis, the vertical distance from the center to the x-axis is equal to the radius. Since the center is at \((-9, -7)\), and the y-coordinate is \(-7\), the radius is \(7\). 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 and \( r \) is the radius. For this problem, \( h = -9 \), \( k = -7 \), and \( r = 7 \). Thus, the standard form of the circle's equation is: \[ (x + 9)^2 + (y + 7)^2 = 49 \]
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