/*! 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 64 Classify the graph of the equati... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 64

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. \(4 x^{2}+25 y^{2}+16 x+250 y+541=0\)

Short Answer

Expert verified
The graph of the given equation is an ellipse.

Step by step solution

01

Regroup terms

Start by grouping x and y variables, we find: \(4(x^2+4x)+25(y^2+10y)=-541\).
02

Simplify the equation

Complete the square for each of the sets of grouped terms. This gives \(4[(x+2)^2 -4]+25[(y+5)^2 -25] = -541\). Simplifying this equation will give \(4(x+2)^2+25(y+5)^2 = 100\)
03

Standard Form

The general form for a ellipse equation is \(\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\), thus, if we express the equation based on the general form for ellipse, we obtain \(\frac{(x+2)^2}{(5/2)^2}+\frac{(y+5)^2}{2^2}=1\)
04

Identify the graph

The equation has the form of an ellipse 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

Identify the conic as a circle or an ellipse. Then find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph. \(\frac{x^{2}}{9}+\frac{y^{2}}{9}=1\)

Sketch the graph of the ellipse, using latera recta. \(9 x^{2}+4 y^{2}=36\)

Find the standard form of the equation of the parabola with the given characteristics. Vertex: (1,2)\(;\) directrix: \(y=-1\)

Use a graphing utility to graph the ellipse. Find the center, foci, and vertices. (Recall that it may be necessary to solve the equation for \(y\) and obtain two equations.) \(36 x^{2}+9 y^{2}+48 x-36 y-72=0\)

Find the eccentricity of the ellipse. \(4 x^{2}+3 y^{2}-8 x+18 y+19=0\)
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

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.