Skip to main content
Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 2 - Graphs and FunctionsProblem 19
Chapter 3, Problem 19

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. center (5, -4), radius 7

Verified step by step guidance
1
Identify the given information: the center of the circle is at the point \( (5, -4) \) and the radius is \( 7 \).
Recall the center-radius form of a circle's equation: \( (x - h)^2 + (y - k)^2 = r^2 \), where \( (h, k) \) is the center and \( r \) is the radius.
Substitute the center coordinates \( h = 5 \) and \( k = -4 \) into the formula: \( (x - 5)^2 + (y - (-4))^2 = r^2 \).
Simplify the expression inside the parentheses: \( (x - 5)^2 + (y + 4)^2 = r^2 \).
Substitute the radius \( r = 7 \) and square it to get \( r^2 = 49 \), so the equation becomes \( (x - 5)^2 + (y + 4)^2 = 49 \). This is the center-radius form of the circle.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equation of a Circle in Center-Radius Form

The center-radius form of a circle's equation is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius. This form directly shows the circle's location and size, making it easier to graph and analyze.
Recommended video:
5:18
Circles in Standard Form

Identifying the Center and Radius

Given the center coordinates (h, k) and radius r, you substitute these values into the center-radius formula. Understanding how to correctly place the center values with opposite signs inside the parentheses is essential for writing the equation accurately.
Recommended video:
05:01
Identifying Intervals of Unknown Behavior

Graphing a Circle

To graph a circle, plot the center point first, then use the radius to mark points in all directions (up, down, left, right) from the center. Connecting these points smoothly forms the circle, helping visualize its size and position on the coordinate plane.
Recommended video:
5:18
Circles in Standard Form
Related Practice
Textbook Question

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-1,3), and (3,4)

1
views
Textbook Question

For each graph, determine whether y is a function of x. Give the domain and range of each relation.

1
views
Textbook Question

Determine whether each relation defines a function, and give the domain and range. {(1,1),(1,-1),(0,0),(2,4),(2,-4)}

Textbook Question

For each piecewise-defined function, find (a) ƒ(-5), (b) ƒ(-1), (c) ƒ(0), and (d) ƒ(3).

f(x)={2+xif x<−4−xif −4≤x≤23xif x>2f(x) =\(\begin{cases}\)2 + x & \(\text{if }\) x < -4 \\-x & \(\text{if }\) -4 \(\leq\) x \(\leq\) 2 \\3x & \(\text{if }\) x > 2\(\end{cases}\)

3
views
Textbook Question

Graph each function. See Examples 1 and 2. ƒ(x)=2/3|x|

5
views
Textbook Question

For the pair of functions defined, find (ƒ+g)(x).Give the domain of each. See Example 2.

ƒ(x)=3x+4, g(x)=2x-5

1
views