Ch. 2 - Graphs and Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 13

Chapter 3, Problem 13

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. center (2, 0), radius 6

Verified step by step guidance

Identify the given information: the center of the circle is at the point (2, 0) and the radius is 6.

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 $(h, k) = (2, 0)$ and the radius $r = 6$ into the formula to get the equation: $ (x - 2)^2 + (y - 0)^2 = 6^2 $.

Simplify the equation by squaring the radius: $ (x - 2)^2 + y^2 = 36 $.

To graph the circle, plot the center at (2, 0), then mark points 6 units away in all directions (up, down, left, right) from the center, and sketch the circle passing through these points.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

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.

Identifying the Center and Radius

Given the center coordinates (h, k) and radius r, you substitute these values into the center-radius formula. For example, with center (2, 0) and radius 6, the equation becomes (x - 2)^2 + (y - 0)^2 = 36.

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. Connect these points smoothly to form the circle, ensuring the radius is consistent throughout.

Recommended video:

5:18

Circles in Standard Form

Related Practice

Textbook Question

Determine the intervals of the domain over which each function is continuous.

views

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 (-5,4), m = -3/2

views

Textbook Question

Let $ƒ (x) = x^{2} + 3$ and $g (x) = - 2 x + 6$ . Find each of the following. See Example 1.

$(ƒ + g) (- 5)$

views

Textbook Question

Let ƒ(x)=x²+3 and g(x)=-2x+6. Find each of the following. (ƒ-g)(-1)

Textbook Question

Determine whether each relation defines a function. {(2,4),(0,2),(2,6)}

Textbook Question

Determine the intervals of the domain over which each function is continuous.

views