/*! 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} Q.21 In Problems 19 鈥�23, identify e... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Q.21 (page 699)

In Problems 19 鈥�23, identify each conic without completing the squares and without applying a rotation of axes.

9x2-12xy+4y2+8x+12y=0

Short Answer

Expert verified

The conic represented by the given equation is a parabola.

Step by step solution

01

Step 1. Given Information

Given to identify the conic without completing the squares and without applying a rotation of axes.

9x2-12xy+4y2+8x+12y=0

02

Step 2. Calculation

An equation of the form Ax2+Bxy+Cy2+Dx+Ey+F=0defines:

  • a parabola if B2-4AC=0
  • an ellipse/ a circle if B2-4AC<0
  • a hyperbola if B2-4AC>0

In the given equation, A=9,B=-12,C=4

Plugging the values:

B2-4AC=-122-494=144-144=0

SinceB2-4AC=0, the conic is a parabola.

03

Step 3. Conclusion

Hence, the conic represented by the given equation is a parabola.

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

Prove that the hyperbola

y2a2-x2b2=1

has the two oblique asymptotesy=abxandy=-abx

True or False

To eliminate the xy-term from the equation x2-2xy+y2-2x+3y+5=0, rotate the axes through an angle 胃, where cot胃=B2-4AC.

Except for degenerate cases, the equation Ax2+Bxy+Cy2+Dx+Ey+F=0defines an__________ if B2-4AC=0.

The Double-angle Formula for the sine function issin2胃=_______.

The graph of a parabola is given. Match graph to its equation.

and equations of the parabola areA)y2=4xC)y2=-4xE)(y-1)2=4(x-1)G)(y-1)2=-4(x-1)B)x2=4yD)x2=-4yF)(x+1)2=4(y+1)H)(x+1)2=4(y+1)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

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.