/*! 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 58 Classify the graph of the equati... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 58

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $$x^{2}+y^{2}-4 x+6 y-3=0$$

Short Answer

Expert verified
The graph of the equation represents a circle

Step by step solution

01

Arrange the equation

Firstly, arrange the equation so that all \(x\) terms and \(y\) terms are together: \(x^{2} - 4x + y^{2} + 6y = 3\)
02

Complete the square for the x and y terms

The next step is to make it the standard form by completing the square for the \(x\) and \(y\) terms. To complete the square, take the coefficient of x, divide by 2 and square it. Do the same for y. Thus, \((x^{2} - 4x + 4) + (y^{2} + 6y + 9) = 3 + 4 + 9\)
03

Convert to standard form

When converted to the standard form of the equation of a circle we get \((x - 2)^{2} + (y + 3)^{2} = 16\)
04

Identify the Conic

Looking at the standard equation, we can conclude that it represents a circle. It fits the format \((x-h)^{2}+(y-k)^{2}=r^{2}\)

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

In Exercises \(91-116\), convert the polar equation to rectangular form. $$r=-2 \cos \theta$$

In Exercises \(71-90,\) convert the rectangular equation to polar form. Assume \(a > 0\). $$3 x+5 y-2=0$$

Determine whether the statement is true or false. Justify your answer. To find the angle between two lines whose angles of inclination \(\theta_{1}\) and \(\theta_{2}\) are known, substitute \(\theta_{1}\) and \(\theta_{2}\) for \(m_{1}\) and \(m_{2},\) respectively, in the formula for the angle between two lines.

Find the distance between the point and the line. Point \((-1,2)\) Line \(5 x+3 y=-4\)

In Exercises \(71-90,\) convert the rectangular equation to polar form. Assume \(a > 0\). $$y^{3}=x^{2}$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

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.