/*! 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 36 Graph \((x-2)^{2}+(y+1)^{2}=9\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Problem 36

Graph \((x-2)^{2}+(y+1)^{2}=9\)

Short Answer

Expert verified
The graph is a circle centered at (2, -1) with a radius of 3.

Step by step solution

01

Identify the Type of Graph

The given equation \((x-2)^{2}+(y+1)^{2}=9\) is in the form of the standard equation of a circle \((x-h)^{2}+(y-k)^{2}=r^{2}\).
02

Determine the Center of the Circle

From the standard equation \((x-h)^{2}+(y-k)^{2}=r^{2}\), compare and identify the center (h, k). Here, \(h = 2\) and \(k = -1\). Thus, the center of the circle is (2, -1).
03

Calculate the Radius

Compare the equation \((x-2)^{2}+(y+1)^{2}=9\) to the standard form. We identify \(r^2 = 9\), so the radius \(r = \sqrt{9} = 3\).
04

Plot the Graph

With the center at (2, -1) and a radius of 3, plot the point (2, -1) on a coordinate plane and draw a circle with a radius of 3 units around this center.

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 equation of a circle
The standard equation of a circle is crucial in understanding how to graph a circle. It is generally written as \( (x-h)^{2}+(y-k)^{2}=r^{2} \). In this form:
\[(x-h)^{2}+(y-k)^{2}=r^{2}\]

Where:
  • \

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

In how many ways can a committee of 3 professors be formed from a department that has 8 professors?

An urn contains 5 white marbles, 10 green marbles, 8 yellow marbles, and 7 black marbles. If one marble is selected, determine the probability that it is white.

Two fair dice are rolled. Determine the probability that the sum of the faces is 3 .

According to a 2016 Gallup survey, \(26 \%\) of U.S. adults visited a casino within the past year. If a U.S. adult is selected at random, what is the probability that he or she has not visited a casino within the past year?

In a certain Algebra and Trigonometry class, there are 18 freshmen and 15 sophomores. Of the 18 freshmen, 10 are male, and of the 15 sophomores, 8 are male. Find the probability that a randomly selected student is: (a) A freshman or female (b) A sophomore or male
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Pure Maths

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.