/*! 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. 43 In Problems 41鈥� 48, find an eq... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Q. 43 (page 668)

In Problems 41鈥� 48, find an equation for the hyperbola described. Graph the equation by hand. Center at (-3,-4); focus at (-3,-8); vertex atrole="math" localid="1647151361836" (-3,-2).

Short Answer

Expert verified

Equation of the hyperbola is:(y+4)24-(x+3)212=1

Graph of the hyperbola is:

Step by step solution

01

Step 1. Given information 

Hyperbola with center at (-3,-4); focus at (-3,-8); vertex at(-3,-2).

02

Step 2. Finding the equation of the hyperbola  

Comparing the given hyperbola with the standard form,

(y-h)2a2-(x-k)2b2=1,b2=c2-a2Center:(h,k)=(-3,-4)Focus:(h,-c+k)=(-3,-8)鈬�c=4Vertex:(h,a+k)=(-3,-2)鈬�a=2b2=c2-a2鈬�b2=42-22鈬�b2=16-4鈬�b2=12鈬�b=卤23

Substituting for h,k,aandbin the standard equation,

(y+4)24-(x+3)212=1

03

Step 3. Graph of the hyperbola 

Equations of asymptotes:

(y-k)=卤ab(x-h)鈬�(y+4)=卤223(x+3)鈬�(y+4)=卤13(x+3)

Graph of the hyperbola is:

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

To graph y=(x+1)2-4, shift the graph of y=x2to the (left/right) _____unit(s) and then (up/down) _____unit(s).

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

A hyperbola for which a=bis called an equilateral hyperbola. Find the eccentricity eof an equilateral hyperbola.

[Note: The eccentricity of a hyperbola is defined in Problem 81.]

Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.

x2=-4y

In Problems 43鈥�52, identify the graph of each equation without applying a rotation of axes.

9x2+12xy+4y2-x-y=0
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

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.