   Chapter 10.1, Problem 39E

Chapter
Section
Textbook Problem

# Sketching a Hyperbola In Exercises 35–40, find the center, foci, and vertices of the hyperbola, and sketch its graph using asymptotes as an aid. x 2 = 9 y 2 + 2 x − 54 y − 80 = 0

To determine

To graph: The hyperbola and find the center, foci and vertices of the hyperbola, x29y2+2x54y80=0.

Explanation

Given:

An equation, x29y2+2x54y80=0.

Graph:

Consider the equation, x29y2+2x54y80=0.

Now, rearrange and rewrite the equation as,

x29y2+2x54y80=0x2+2x+19(y26y9)=181+80(x+1)29(y+3)2=09(y+3)2=(x+1)2

On further simplification,

9(y+3)2=(x+1)2y+3=±13(x+1)y=3±13(x+1)

Thus, the equation, x29y2+2x54y80=0 is of a degenerate hyperbola represented by two lines, y=3+13(x+1) and y=313(x+1).

In order to plot the lines, make a coordinate table for both the lines, y=3+13(x+1) and y=313(x+1)

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Given that the point P(3, 5) lies on the line kx + 3y + 9 = 0, find k.

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In Exercises 3-6, simplify the expression. (14)x3/4

Calculus: An Applied Approach (MindTap Course List)

#### Solve the equations in Exercises 126. x69x4=0

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Simplify each expression. 24

Trigonometry (MindTap Course List) 