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
![**College Algebra: Homework - Question 5, 2.2.23 (Part 1 of 2)**
**Task:**
Use the graph below to determine the equation of the circle in (a) center-radius form and (b) general form.
**Graph Explanation:**
The image shows a coordinate plane with a circle centered at the point (4, 4). The circle passes through the point (4, 8). This indicates that the radius of the circle is the distance from (4, 4) to (4, 8), which is 4 units.
**Steps to Determine the Equation:**
1. **Center-Radius Form:**
The equation of a circle in center-radius form is \((x-h)^2 + (y-k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is the radius.
- Center \((h, k)\): (4, 4)
- Radius \(r\): 4
Substituting these values into the form, the equation becomes:
\((x-4)^2 + (y-4)^2 = 4^2\)
\((x-4)^2 + (y-4)^2 = 16\)
2. **General Form:**
Expanding the center-radius form into the general form, the equation \((x-4)^2 + (y-4)^2 = 16\) needs to be expanded.
- Expand:
\[x^2 - 8x + 16 + y^2 - 8y + 16 = 16\]
- Simplify to obtain the general form:
\[x^2 + y^2 - 8x - 8y + 16 = 0\]
Thus, the equations of the circle are:
- (a) Center-Radius Form: \((x-4)^2 + (y-4)^2 = 16\)
- (b) General Form: \(x^2 + y^2 - 8x - 8y + 16 = 0\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84f905e7-8d15-44f1-8ba1-68b7e3fd4c33%2F1b29476c-0409-4ed6-bdc8-4343e166103c%2F31qy37w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**College Algebra: Homework - Question 5, 2.2.23 (Part 1 of 2)**
**Task:**
Use the graph below to determine the equation of the circle in (a) center-radius form and (b) general form.
**Graph Explanation:**
The image shows a coordinate plane with a circle centered at the point (4, 4). The circle passes through the point (4, 8). This indicates that the radius of the circle is the distance from (4, 4) to (4, 8), which is 4 units.
**Steps to Determine the Equation:**
1. **Center-Radius Form:**
The equation of a circle in center-radius form is \((x-h)^2 + (y-k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is the radius.
- Center \((h, k)\): (4, 4)
- Radius \(r\): 4
Substituting these values into the form, the equation becomes:
\((x-4)^2 + (y-4)^2 = 4^2\)
\((x-4)^2 + (y-4)^2 = 16\)
2. **General Form:**
Expanding the center-radius form into the general form, the equation \((x-4)^2 + (y-4)^2 = 16\) needs to be expanded.
- Expand:
\[x^2 - 8x + 16 + y^2 - 8y + 16 = 16\]
- Simplify to obtain the general form:
\[x^2 + y^2 - 8x - 8y + 16 = 0\]
Thus, the equations of the circle are:
- (a) Center-Radius Form: \((x-4)^2 + (y-4)^2 = 16\)
- (b) General Form: \(x^2 + y^2 - 8x - 8y + 16 = 0\)
Expert Solution
Step 2
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education