/*! 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 39 How many points are there on the... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 39

How many points are there on the graph of \((x-4)^{2}+(y-1)^{2}=0 ?\)

Short Answer

Expert verified
There is 1 point on the graph.

Step by step solution

01

Understand the Given Equation

The given equation \((x-4)^{2}+(y-1)^{2}=0\) represents a circle equation in the standard form \((x-h)^{2}+(y-k)^{2}=r^{2}\).
02

Identify the Center and Radius

In the equation \((x-4)^{2}+(y-1)^{2}=0\), the center of the circle is \((4, 1)\), and the radius is \sqrt{0} = 0\.
03

Interpret the Radius

Since the radius of the circle is 0, the 'circle' is actually a single point at the center \((4, 1)\).
04

Determine the Number of Points

There is only one point on this 'circle,' which is the center point itself \((4, 1)\).

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.

Circle Equations
A circle can be defined algebraically using an equation in standard form: \( (x-h)^2+(y-k)^2=r^2 \).
Here:
  • \

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

Graph each system of inequalities. \(x+y>1\) \(y \geq 2 x-2\) \(y \leq 4\)

Solve each system using the elimination method or a combination of the elimination and substitution methods. $$ \begin{array}{l} 2 x^{2}=8-2 y^{2} \\ 3 x^{2}=24-4 y^{2} \end{array} $$

Graph each system of inequalities. \(y \leq-x^{2}\) \(y \geq x-3\) \(y \leq-1\) \(x<1\)

Solve each system using the substitution method. $$ \begin{array}{l} x y=-5 \\ 2 x+y=3 \end{array} $$

Write the center-radius form of each circle described. Then graph the circle. $$ \text { Center: }(-3,2) ; \text { radius: } 3 $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Decision 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.