Q. 21 Complete the square to describe ... [FREE SOLUTION]

Chapter 9: Q. 21 (page 772)

Complete the square to describe the conics in Exercises 18鈥�21 .
$y^{2} - 8 y - 4 x^{2} - 8 x - 13 = 0$

Short Answer

Expert verified

The answer is $\frac{(y - 4)^{2}}{25} - \frac{4 (x + 1)^{2}}{25} = 1 {H y p e r b o l a}$ with center $(- 1, 4)$ that opens up and down.

Step by step solution

Step 1. Given Information.

The equation is $y^{2} - 8 y - 4 x^{2} - 8 x - 13 = 0$ .

Step 2. Completing the square.

Now,

$(y^{2} - 8 y) - (4 x^{2} + 8 x) - 13 = 0 (y^{2} - 8 y) - 4 (x^{2} + 2 x) - 13 = 0 (y^{2} - 8 y + 16 - 16) - 4 (x^{2} + 2 x + 1 - 1) - 13 = 0 (y^{2} - 8 y + 16) - 16 - 4 (x^{2} + 2 x + 1) + 4 - 13 = 0 (y^{2} - 8 y + 16) - 4 (x^{2} + 2 x + 1) - 25 = 0 (y - 4)^{2} - 4 {(x^{2} + 1)}^{2} - 25 = 0$

Step 3. Final equation.

On simplifying the above equation,

$(y - 4)^{2} - 4 {(x^{2} + 1)}^{2} - 25 + 25 = 0 + 25 (y - 4)^{2} - 4 {(x^{2} + 1)}^{2} = 25 \frac{(y - 4)^{2} - 4 (x + 1)^{2}}{25} = \frac{25}{25} \frac{(y - 4)^{2} - 4 (x + 1)^{2}}{25} = 1 \frac{(y - 4)^{2}}{25} - \frac{4 (x + 1)^{2}}{25} = 1$

which is a hyperbola with center $(- 1, 4)$ that opens up and down.

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

Complete the square to describe the conics in Exercises 18鈥�21 .
$y^{2} - 8 y - 4 x^{2} - 8 x - 13 = 0$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Completing the square.

Step 3. Final equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

91影视

Complete the square to describe the conics in Exercises 18鈥�21 .y2-8y-4x2-8x-13=0

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Completing the square.

Step 3. Final equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

Complete the square to describe the conics in Exercises 18鈥�21 .
$y^{2} - 8 y - 4 x^{2} - 8 x - 13 = 0$