Open In App

Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 10: Q43. (page 677)

In Problems 43–52, identify the graph of each equation without applying a rotation of axes. $x^{2} + 3 x y - 2 y^{2} + 3 x + 2 y + 5 = 0$

Short Answer

Expert verified

The equation defines hyperbola.

Step by step solution

Step 1. Given Information

The given equation is $x^{2} + 3 x y - 2 y^{2} + 3 x + 2 y + 5 = 0$

Here $A = 1, B = 3, C = - 2$

Step 2. Identifying Conic

$B^{2} - 4 A C = 3^{2} - 4 (1) (- 2) B^{2} - 4 A C = 9 + 8 = 17 > 0$

The equation defines hyperbola.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Except for degenerate cases, the equation $A x^{2} + B x y + C y^{2} + D x + E y + F = 0$ defines $a (n)__________$ if $B^{2} - 4 A C = 0$ .

In Problems 31– 42, rotate the axes so that the new equation contains no $x y$ -term. Analyze and graph the new equation. Refer to Problems 21–30 for Problems 31– 40.

5 x^{2} + 6 x y + 5 y^{2} - 8 = 0

Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.

$y^{2} = 8 x$

The distance $d$ from $P_{1} = (2, - 5)$ to $P_{2} = (4, - 2)$ is $d =________$ .

In Problem, identify the graph of each equation without completing the squares.

$2 x^{2} + y^{2} - 8 x + 4 y + 2 = 0$

See all solutions

Recommended explanations on Math Textbooks

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free

In Problems 43–52, identify the graph of each equation without applying a rotation of axes. $x^{2} + 3 x y - 2 y^{2} + 3 x + 2 y + 5 = 0$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Identifying Conic

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Pure Maths

Calculus

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Company

Product

Help

In Problems 43–52, identify the graph of each equation without applying a rotation of axes.x2+3xy-2y2+3x+2y+5=0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Identifying Conic

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Pure Maths

Calculus

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problems 43–52, identify the graph of each equation without applying a rotation of axes. $x^{2} + 3 x y - 2 y^{2} + 3 x + 2 y + 5 = 0$