**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)
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,...
Related questions
Question
![**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:
\[
(x + 9)^2 + (y + 7)^2 = 49
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F323a188d-72c2-4f77-bbb3-3034e58495c9%2F31d5f56b-0ee2-49ae-bd4b-5c54a6ec59ab%2Fc0ry2pc.jpeg&w=3840&q=75)
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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