Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Show that the sum of the $ x- $ and $ y- $ interc…

02:37

Question

Answered step-by-step

Problem 45 Hard Difficulty

Find an equation of the tangent line to the hyperbola
$ \frac {x^2}{a^2} - \frac {y^2}{b^2} = 1 $
at the point $ (x_o, y_o). $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Doruk Isik
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Doruk Isik

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

01:38

Frank Lin

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Related Topics

Derivatives

Differentiation

Discussion

You must be signed in to discuss.
Top Calculus 1 / AB Educators
Grace He
Catherine Ross

Missouri State University

Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

Join Course
Recommended Videos

05:00

Find an equation of the li…

02:21

Tangent lines for a hyperb…

01:23

Use implicit differentiati…

02:49

Find an equation of the ta…

Watch More Solved Questions in Chapter 3

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80

Video Transcript

In this problem, we are given an equation and were asked to find an equation of potential line for line or not. We know that the question of the line will be for y minus t is equal to the slope or the derivatur of this function. It will be a given point of p by x minus x. Not so we first need to torquay the derivative at this given point. So, let's differentiate this given equation, we have 2 x over a square minus 2 y over b squared times y prime is equal to 0 point from this. Then we see that y prime is equal to x over a square times v squared over y, or we can write this 1. As if you were to relate the given point, we would find y prime to be equal to b squared over a squared mltiplied by x, not over y, not now. If that is why primeve point, let's right, equal structor, tangent line again, we have 1 minus 1. Is equal to b squared over a squared times x, not over? Why not multiplied by x minus x? Not now, let's multiply both sides by a square times y, not we would end up with a square times y, not times y minus a square times y. Not squared, is equal to b squared x, not times x, minus b, squared x, not square. We can write further this 1 as a square y, not times y minus b, squared x, not times x, that is equal to v square that is equal to b squared x, not squared minus 8 squad y, not squared all right. Well, that should be the other way around. This should be a square y, not squared minus b squared x, not square all right now, if we divide both sides by a square times b squared, he would end up with x, not or y, not times y divided by b, squared minus x, not times x, Divided by a square is equal to y, not squared, divided by b square minus x, not squared divided by a all right. This is same as x, not times x. Over a squared minus y, not times y over b squared, is equal to x, not squared over a square plus or minus y, not squared over square. So basically, i multiply both sides by negative 1 point. Now, look at the right hand, side here and look at the original equation. If you plugged given point x and a 1 into the original question, it would end up with 1 and since right hand. Side is the same. We'Re going to say that right hand. Side is equal to 1 side of the equation of the tangent line is x not times x, divided by a square minus y, not times y divided by b. Squared is equal to 1.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
84
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
53
Hosted by: Alonso M
See More

Related Topics

Derivatives

Differentiation

Top Calculus 1 / AB Educators
Grace He

Numerade Educator

Catherine Ross

Missouri State University

Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

Join Course
Recommended Videos

05:00

Find an equation of the line tangent to the hyperbola $\frac{x^{2}}{a^{2}}-\fra…

02:21

Tangent lines for a hyperbola Find an equation of the line tangent to the hyper…

01:23

Use implicit differentiation to find an equation of the tangent line to the cur…

02:49

Find an equation of the tangent line to the hyperbola x2 / a2 − y2 / b2 = 1 at …
Additional Mathematics Questions

02:16

In a theatre there is a central block of seats with n seats per row: Blocks …

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started