/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 18 Graph each circle. Identify the ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 18

Graph each circle. Identify the center if it is not at the origin. $$ x^{2}+y^{2}=4 $$

Short Answer

Expert verified
The center is at the origin (0, 0) and the radius is 2 units.

Step by step solution

01

Identify the standard form of a circle's equation

Compare the given equation with the standard form of the circle's equation, which is \[ (x-h)^2 + (y-k)^2 = r^2 \].
02

Rewrite the given equation

The given equation is \[ x^2 + y^2 = 4 \]. No terms need to be moved; the equation is already in standard form.
03

Identify the center and radius

Identify the values of \(h\), \(k\), and \(r\) from the standard form. Here, \(h = 0\), \(k = 0\), and \(r^2 = 4\), so \(r = 2\).
04

Graph the circle

Draw a coordinate plane. Plot the center of the circle at the origin (0, 0). From the center, measure a radius of 2 units in all directions (up, down, left, right), and draw the circle connecting these points.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

standard form of a circle
Understanding the standard form of a circle's equation is essential for graphing and analyzing circles in algebra. The standard form of a circle equation is given by: ( x - h ) ^2 + ( y - k ) ^2 = r^2 Here鈥檚 what each term represents: - (h, k) is the center of the circle. - 鈥榬鈥� is the radius of the circle. To recognize a circle and identify its key components, you should always refer to this standard form.
circle equation
In math class, the circle equation is an important concept to understand and applies to various problems. When looking at an equation, compare it to the standard form ( x - h ) ^2 + ( y - k ) ^2 = r^2 . For the given problem, the equation is: x^2 + y^2 = 4 This equation is already in the standard form, with h and k being zero (since (x-0) and (y-0) don't need to be written). Knowing how to match your given equation with the standard form makes it easier to identify other key details.
identifying center and radius
After you have the circle equation in standard form, it鈥檚 time to identify the center and radius. From the given equation: x^2 + y^2 = 4 We can identify: The center (h, k) is (0, 0). The radius r is the square root of 4, which is 2. Graphing the circle becomes straightforward. Simply plot the center at the origin (0, 0). From this point, measure 2 units in all directions to mark the edge of the circle. Draw the curve connecting these points, and you have graphed your circle. Identifying the center and radius quickly can save time and simplify various problems in algebra dynamics.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use the shading feature of a graphing calculator to graph each system. $$ \begin{aligned} &y-3 \end{aligned} $$

Find the equation of a circle satisfying the given conditions. Center: \((-8,-5) ;\) radius: \(\sqrt{5}\)

Solve each system by the substitution method. $$ \begin{aligned} &x^{2}-x y+y^{2}=0\\\ &x-2 y=1 \end{aligned} $$

Find the \(x\) - and \(y\) -intercepts of the graph of \(4 x+3 y=12\)

Solve each system by the elimination method or a combination of the elimination and substi- tution methods. $$ \begin{array}{l} {3 x^{2}+2 x y-3 y^{2}=5} \\ {-x^{2}-3 x y+y^{2}=3} \end{array} $$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.