**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,...
icon
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:

\[
(x + 9)^2 + (y + 7)^2 = 49
\]
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: \[ (x + 9)^2 + (y + 7)^2 = 49 \]
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education