Chapter 10: Q54. (page 677)

Show that $A + C = A' + C'$ , and thus show that $A + C$ is invariant; that is, its value does not change under a rotation of axes.

Short Answer

Expert verified

Thus, $A + C = A' + C'$ is invariant.

Step by step solution

Step 1. Given Information

$A x^{2} + B x y + C y^{2} + D x + E y + F = 0$

Step 2. Explanation to invariant

Consider the equation $x^{2} + 4 x y + 4 y^{2} + 5 \sqrt{5} y + 5 = 0$

Here $A = 1, C = 4$ gives $A + C = 1 + 4 = 5$

The rotated equation is $0 x'^{2} + 5 y'^{2} - 2.3 \sqrt{5} x' + 4.4 \sqrt{5} y' + 5 = 0$

Here $A' = 0, C' = 5$ gives $A' + C' = 5$

Both $A + C$ and $A' + C'$ are equal.

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!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Show that $A + C = A' + C'$ , and thus show that $A + C$ is invariant; that is, its value does not change under a rotation of axes.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation to invariant

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Decision Maths

Calculus

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Show thatA+C=A'+C', and thus show that A+Cis invariant; that is, its value does not change under a rotation of axes.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation to invariant

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Decision Maths

Calculus

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Show that $A + C = A' + C'$ , and thus show that $A + C$ is invariant; that is, its value does not change under a rotation of axes.