/*! 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 53 Identify the quadric surface. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 53

Identify the quadric surface. $$ 3 z=-y^{2}+x^{2} $$

Short Answer

Expert verified
The given equation represents a hyperbolic paraboloid.

Step by step solution

01

Examine the Equation

To identify the type of quadric surface, you first need to examine the equation \( 3z = -y^2 + x^2 \). The equation can also be rearranged to bring it to a more standard form, as \( z = (-y^2 + x^2)/3 \).
02

Identify the Quadratic Terms

Focus on the quadratic terms of the equation. It is clear that the signs are opposite, which will help identify the quadric surface type. When the signs of the square terms in the equation are opposite, it typically represents a hyperbolic paraboloid.
03

Confirm Hyperbolic Paraboloid

The equation \( z = \frac{1}{3}(x^2 - y^2) \) confirms it is a hyperbolic paraboloid. In the standard form of the equation for a hyperbolic paraboloid \( z = \frac{1}{a^2}x^2 - \frac{1}{b^2}y^2 \), the coefficients of \( x^2 \) and \( y^2 \) are of opposite signs, just as in our given 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

Use a symbolic integration utility to evaluate the double integral. $$ \int_{0}^{2} \int_{\sqrt{4-x^{2}}}^{4-x^{2} / 4} \frac{x y}{x^{2}+y^{2}+1} d y d x $$

Use the regression capabilities of a graphing utility or a spreadsheet to find the least squares regression quadratic for the given points. Then plot the points and graph the least squares regression quadratic. $$ (-4,5),(-2,6),(2,6),(4,2) $$

Sketch the region of integration and evaluate the double integral. $$ \int_{-a}^{a} \int_{-\sqrt{a^{2}-x^{2}}}^{\sqrt{a^{2-x^{2}}}} d y d x $$

Use the regression capabilities of a graphing utility or a spreadsheet to find the least squares regression quadratic for the given points. Then plot the points and graph the least squares regression quadratic. $$ (-2,0),(-1,0),(0,1),(1,2),(2,5) $$

Sketch the region \(R\) whose area is given by the double integral. Then change the order of integration and show that both orders yield the same area. $$ \int_{0}^{1} \int_{0}^{2} d y d x $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

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.