/*! 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 81 Does \((x-3)^{2}+(y-5)^{2}=-25\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 81

Does \((x-3)^{2}+(y-5)^{2}=-25\) represent the equation of a circle? What sort of set is the graph of this equation?

Short Answer

Expert verified
The graph of the equation \((x-3)^{2}+(y-5)^{2}=-25\) does not represent a circle, instead it represents an empty set. This equation has no real solutions because a square of a real number can never be negative.

Step by step solution

01

Identify the standard form of a circle

The equation of a circle in its standard form is \((x-h)^{2}+(y-k)^{2}=r^2\), in which \((h,k)\) are the coordinates of the center of the circle and \(r\) is the radius of circle. The values of \(r^2\) or the square of radius must be non-negative. It means, \(r^2 >= 0\).
02

Analyze the given equation

In the given equation \((x-3)^{2}+(y-5)^{2}=-25\), instead of being positive or zero, the value on the right side, stating the square of radius, is negative. The value \(-25\) goes against the requirement \(r^2 >= 0\) in the standard form of a circle. Therefore, this equation cannot be for a circle.
03

Identify the graph of the equation

Equations with negative values for the radius squared have no real solutions, because the square of any real number is never negative. Thus, it represents an empty set or null set. There are no points \((x,y)\) in the Cartesian coordinate system that would satisfy this equation.

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!

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

How do you determine if an equation in \(x\) and \(y\) defines \(y\) as a function of \(x ?\)

use a graphing utility to graph each circle whose equation is given. $$ x^{2}+y^{2}=25 $$

complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$ x^{2}+y^{2}+12 x-6 y-4=0 $$

What is a circle? Without using variables, describe how the definition of a circle can be used to obtain a form of its equation.

What does it mean if a function \(f\) is increasing on an interval?
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Mechanics Maths

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.