Q 22. In Problem, determine the approp... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 10: Q 22. (page 677)

In Problem, determine the appropriate rotation formulas to use so that the new equation contains no $x y -$ term.
width="139">x2-4xy+y2-3=0

Short Answer

Expert verified

$x = \frac{x^{'}}{\sqrt{2}} - \frac{y^{'}}{\sqrt{2}} y = \frac{x^{'}}{\sqrt{2}} + \frac{y^{'}}{\sqrt{2}}$

Step by step solution

Step 1. Given information

An equation is $x^{2} - 4 x y + y^{2} - 3 = 0$ .

Step 2. Determine the appropriate rotation formulas.

The given conic is given by the equation given below.

$x^{2} - 4 x y + y^{2} - 3 = 0$

The rotation formulae for the given conic such that $x y -$ term is absent are given by the formulae given below, where $胃$ can be determined by the relation $\cot 2 胃 = \frac{A - C}{B}$ .

$x = x^{'} \cos 胃 - y^{'} \sin 胃 y = x^{'} \sin 胃 + y^{'} \cos 胃$

The value of the $胃$ can be determined by substituting the values of $A, B, C$ in the expression that evaluates the value of angle $胃$ .

$\begin{array}{rcl} \cot 2 胃 & = & \frac{1 - 1}{- 4} \\ = & 0 \end{array}$

$2 胃 = \frac{蟺}{4}$

Therefore the rotation formulae for the given equation of conic are given by the equations that follow

width="155">x=x'cos蟺4-y'sin蟺4=x'2-y'2

$\begin{array}{rcl} y & = & x^{'} \sin \frac{蟺}{4} + y^{'} \cos \frac{蟺}{4} \\ = & \frac{x^{'}}{\sqrt{2}} + \frac{y^{'}}{\sqrt{2}} \end{array}$

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

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

In Problem, determine the appropriate rotation formulas to use so that the new equation contains no $x y -$ term.
width="139">x2-4xy+y2-3=0

Short Answer

Step by step solution

Step 1. Given information

Step 2. Determine the appropriate rotation formulas.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Calculus

Discrete Mathematics

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

91影视

In Problem, determine the appropriate rotation formulas to use so that the new equation contains no xy-term.width="139">x2-4xy+y2-3=0

Short Answer

Step by step solution

Step 1. Given information

Step 2. Determine the appropriate rotation formulas.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Calculus

Discrete Mathematics

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

In Problem, determine the appropriate rotation formulas to use so that the new equation contains no $x y -$ term.
width="139">x2-4xy+y2-3=0