BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Find an equation of the tangent line to the hyperbola

x 2 a 2 y 2 b 2 = 1

at the point ( x 0 , y 0 ) .

To determine

To find:

Equation of tangent line to hyperbola at the point x0,y0

Explanation

1) Formula:

ddxxn=nxn-1

2) Given:

x2a2-y2b2=1

3) Calculation:

Slope of tangent at a point is the derivative with respect to x at that point, So let us differentiate the curve with respect to x

ddxx2a2-y2b2=1

ddxx2a2-ddxy2b2=ddx1

1a2ddxx2-1b2ddxy2=ddx1

2xa2-2yb2dydx=0

xa2-yb2dydx=0 Thus we have

-yb2dydx=-xa2

dydx=xb2ya2

Slop of tangent at

x0,y0=dydxx0,y0=x0b2y0a2

Slope

m =x0b2y0a2

Use point slope form to obtain an equation of line,

Equation of tangent at x0,y0 is

y-y0y0a2=x0b2(x-x0)

yy0a2-y0

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
Sect-2.1 P-11ESect-2.1 P-12ESect-2.1 P-13ESect-2.1 P-14ESect-2.1 P-15ESect-2.1 P-16ESect-2.1 P-17ESect-2.1 P-18ESect-2.1 P-19ESect-2.1 P-20ESect-2.1 P-21ESect-2.1 P-22ESect-2.1 P-23ESect-2.1 P-24ESect-2.1 P-25ESect-2.1 P-26ESect-2.1 P-27ESect-2.1 P-28ESect-2.1 P-29ESect-2.1 P-30ESect-2.1 P-31ESect-2.1 P-32ESect-2.1 P-33ESect-2.1 P-34ESect-2.1 P-35ESect-2.1 P-36ESect-2.1 P-37ESect-2.1 P-38ESect-2.1 P-39ESect-2.1 P-40ESect-2.1 P-41ESect-2.1 P-42ESect-2.1 P-43ESect-2.1 P-44ESect-2.1 P-45ESect-2.1 P-46ESect-2.1 P-47ESect-2.1 P-48ESect-2.1 P-49ESect-2.1 P-50ESect-2.1 P-51ESect-2.1 P-52ESect-2.1 P-53ESect-2.1 P-54ESect-2.1 P-55ESect-2.1 P-56ESect-2.1 P-57ESect-2.1 P-58ESect-2.1 P-59ESect-2.1 P-60ESect-2.1 P-61ESect-2.2 P-1ESect-2.2 P-2ESect-2.2 P-3ESect-2.2 P-4ESect-2.2 P-5ESect-2.2 P-6ESect-2.2 P-7ESect-2.2 P-8ESect-2.2 P-9ESect-2.2 P-10ESect-2.2 P-11ESect-2.2 P-12ESect-2.2 P-13ESect-2.2 P-14ESect-2.2 P-15ESect-2.2 P-16ESect-2.2 P-17ESect-2.2 P-18ESect-2.2 P-19ESect-2.2 P-20ESect-2.2 P-21ESect-2.2 P-22ESect-2.2 P-23ESect-2.2 P-24ESect-2.2 P-25ESect-2.2 P-26ESect-2.2 P-27ESect-2.2 P-28ESect-2.2 P-29ESect-2.2 P-30ESect-2.2 P-31ESect-2.2 P-32ESect-2.2 P-33ESect-2.2 P-34ESect-2.2 P-35ESect-2.2 P-36ESect-2.2 P-37ESect-2.2 P-38ESect-2.2 P-39ESect-2.2 P-40ESect-2.2 P-41ESect-2.2 P-42ESect-2.2 P-43ESect-2.2 P-44ESect-2.2 P-45ESect-2.2 P-46ESect-2.2 P-47ESect-2.2 P-48ESect-2.2 P-49ESect-2.2 P-50ESect-2.2 P-51ESect-2.2 P-52ESect-2.2 P-53ESect-2.2 P-54ESect-2.2 P-55ESect-2.2 P-56ESect-2.2 P-57ESect-2.2 P-58ESect-2.2 P-59ESect-2.2 P-60ESect-2.2 P-61ESect-2.2 P-62ESect-2.2 P-63ESect-2.2 P-64ESect-2.2 P-65ESect-2.3 P-1ESect-2.3 P-2ESect-2.3 P-3ESect-2.3 P-4ESect-2.3 P-5ESect-2.3 P-6ESect-2.3 P-7ESect-2.3 P-8ESect-2.3 P-9ESect-2.3 P-10ESect-2.3 P-11ESect-2.3 P-12ESect-2.3 P-13ESect-2.3 P-14ESect-2.3 P-15ESect-2.3 P-16ESect-2.3 P-17ESect-2.3 P-18ESect-2.3 P-19ESect-2.3 P-20ESect-2.3 P-21ESect-2.3 P-22ESect-2.3 P-23ESect-2.3 P-24ESect-2.3 P-25ESect-2.3 P-26ESect-2.3 P-27ESect-2.3 P-28ESect-2.3 P-29ESect-2.3 P-30ESect-2.3 P-31ESect-2.3 P-32ESect-2.3 P-33ESect-2.3 P-34ESect-2.3 P-35ESect-2.3 P-36ESect-2.3 P-37ESect-2.3 P-38ESect-2.3 P-39ESect-2.3 P-40ESect-2.3 P-41ESect-2.3 P-42ESect-2.3 P-43ESect-2.3 P-44ESect-2.3 P-45ESect-2.3 P-46ESect-2.3 P-47ESect-2.3 P-48ESect-2.3 P-49ESect-2.3 P-50ESect-2.3 P-51ESect-2.3 P-52ESect-2.3 P-53ESect-2.3 P-54ESect-2.3 P-55ESect-2.3 P-56ESect-2.3 P-57ESect-2.3 P-58ESect-2.3 P-59ESect-2.3 P-60ESect-2.3 P-61ESect-2.3 P-62ESect-2.3 P-63ESect-2.3 P-64ESect-2.3 P-65ESect-2.3 P-66ESect-2.3 P-67ESect-2.3 P-68ESect-2.3 P-69ESect-2.3 P-70ESect-2.3 P-71ESect-2.3 P-72ESect-2.3 P-73ESect-2.3 P-74ESect-2.3 P-75ESect-2.3 P-76ESect-2.3 P-77ESect-2.3 P-78ESect-2.3 P-79ESect-2.3 P-80ESect-2.3 P-81ESect-2.3 P-82ESect-2.3 P-83ESect-2.3 P-84ESect-2.3 P-85ESect-2.3 P-86ESect-2.3 P-87ESect-2.3 P-88ESect-2.3 P-89ESect-2.3 P-90ESect-2.3 P-91ESect-2.3 P-92ESect-2.3 P-93ESect-2.3 P-94ESect-2.3 P-95ESect-2.3 P-96ESect-2.3 P-97ESect-2.3 P-98ESect-2.3 P-99ESect-2.3 P-100ESect-2.3 P-101ESect-2.3 P-102ESect-2.3 P-103ESect-2.3 P-104ESect-2.3 P-105ESect-2.3 P-106ESect-2.3 P-107ESect-2.3 P-108ESect-2.3 P-109ESect-2.3 P-110ESect-2.4 P-1ESect-2.4 P-2ESect-2.4 P-3ESect-2.4 P-4ESect-2.4 P-5ESect-2.4 P-6ESect-2.4 P-7ESect-2.4 P-8ESect-2.4 P-9ESect-2.4 P-10ESect-2.4 P-11ESect-2.4 P-12ESect-2.4 P-13ESect-2.4 P-14ESect-2.4 P-15ESect-2.4 P-16ESect-2.4 P-17ESect-2.4 P-18ESect-2.4 P-19ESect-2.4 P-20ESect-2.4 P-21ESect-2.4 P-22ESect-2.4 P-23ESect-2.4 P-24ESect-2.4 P-25ESect-2.4 P-26ESect-2.4 P-27ESect-2.4 P-28ESect-2.4 P-29ESect-2.4 P-30ESect-2.4 P-31ESect-2.4 P-32ESect-2.4 P-33ESect-2.4 P-34ESect-2.4 P-35ESect-2.4 P-36ESect-2.4 P-37ESect-2.4 P-38ESect-2.4 P-39ESect-2.4 P-40ESect-2.4 P-41ESect-2.4 P-42ESect-2.4 P-43ESect-2.4 P-44ESect-2.4 P-45ESect-2.4 P-46ESect-2.4 P-47ESect-2.4 P-48ESect-2.4 P-49ESect-2.4 P-50ESect-2.4 P-51ESect-2.4 P-52ESect-2.4 P-53ESect-2.4 P-54ESect-2.4 P-55ESect-2.4 P-56ESect-2.4 P-57ESect-2.4 P-58ESect-2.5 P-1ESect-2.5 P-2ESect-2.5 P-3ESect-2.5 P-4ESect-2.5 P-5ESect-2.5 P-6ESect-2.5 P-7ESect-2.5 P-8ESect-2.5 P-9ESect-2.5 P-10ESect-2.5 P-11ESect-2.5 P-12ESect-2.5 P-13ESect-2.5 P-14ESect-2.5 P-15ESect-2.5 P-16ESect-2.5 P-17ESect-2.5 P-18ESect-2.5 P-19ESect-2.5 P-20ESect-2.5 P-21ESect-2.5 P-22ESect-2.5 P-23ESect-2.5 P-24ESect-2.5 P-25ESect-2.5 P-26ESect-2.5 P-27ESect-2.5 P-28ESect-2.5 P-29ESect-2.5 P-30ESect-2.5 P-31ESect-2.5 P-32ESect-2.5 P-33ESect-2.5 P-34ESect-2.5 P-35ESect-2.5 P-36ESect-2.5 P-37ESect-2.5 P-38ESect-2.5 P-39ESect-2.5 P-40ESect-2.5 P-41ESect-2.5 P-42ESect-2.5 P-43ESect-2.5 P-44ESect-2.5 P-45ESect-2.5 P-46ESect-2.5 P-47ESect-2.5 P-48ESect-2.5 P-49ESect-2.5 P-50ESect-2.5 P-51ESect-2.5 P-52ESect-2.5 P-53ESect-2.5 P-54ESect-2.5 P-55ESect-2.5 P-56ESect-2.5 P-57ESect-2.5 P-58ESect-2.5 P-59ESect-2.5 P-60ESect-2.5 P-61ESect-2.5 P-62ESect-2.5 P-63ESect-2.5 P-64ESect-2.5 P-65ESect-2.5 P-66ESect-2.5 P-67ESect-2.5 P-68ESect-2.5 P-69ESect-2.5 P-70ESect-2.5 P-71ESect-2.5 P-72ESect-2.5 P-73ESect-2.5 P-74ESect-2.5 P-75ESect-2.5 P-76ESect-2.5 P-77ESect-2.5 P-78ESect-2.5 P-79ESect-2.5 P-80ESect-2.5 P-81ESect-2.5 P-82ESect-2.5 P-83ESect-2.5 P-84ESect-2.5 P-85ESect-2.5 P-86ESect-2.5 P-87ESect-2.5 P-88ESect-2.5 P-89ESect-2.5 P-90ESect-2.6 P-1ESect-2.6 P-2ESect-2.6 P-3ESect-2.6 P-4ESect-2.6 P-5ESect-2.6 P-6ESect-2.6 P-7ESect-2.6 P-8ESect-2.6 P-9ESect-2.6 P-10ESect-2.6 P-11ESect-2.6 P-12ESect-2.6 P-13ESect-2.6 P-14ESect-2.6 P-15ESect-2.6 P-16ESect-2.6 P-17ESect-2.6 P-18ESect-2.6 P-19ESect-2.6 P-20ESect-2.6 P-21ESect-2.6 P-22ESect-2.6 P-23ESect-2.6 P-24ESect-2.6 P-25ESect-2.6 P-26ESect-2.6 P-27ESect-2.6 P-28ESect-2.6 P-29ESect-2.6 P-30ESect-2.6 P-31ESect-2.6 P-32ESect-2.6 P-33ESect-2.6 P-34ESect-2.6 P-35ESect-2.6 P-36ESect-2.6 P-37ESect-2.6 P-38ESect-2.6 P-39ESect-2.6 P-40ESect-2.6 P-41ESect-2.6 P-42ESect-2.6 P-43ESect-2.6 P-44ESect-2.6 P-45ESect-2.6 P-46ESect-2.6 P-47ESect-2.6 P-48ESect-2.6 P-49ESect-2.6 P-50ESect-2.6 P-51ESect-2.6 P-52ESect-2.6 P-53ESect-2.6 P-54ESect-2.6 P-55ESect-2.6 P-56ESect-2.6 P-57ESect-2.6 P-58ESect-2.6 P-59ESect-2.6 P-60ESect-2.6 P-61ESect-2.6 P-62ESect-2.7 P-1ESect-2.7 P-2ESect-2.7 P-3ESect-2.7 P-4ESect-2.7 P-5ESect-2.7 P-6ESect-2.7 P-7ESect-2.7 P-8ESect-2.7 P-9ESect-2.7 P-10ESect-2.7 P-11ESect-2.7 P-12ESect-2.7 P-13ESect-2.7 P-14ESect-2.7 P-15ESect-2.7 P-16ESect-2.7 P-17ESect-2.7 P-18ESect-2.7 P-19ESect-2.7 P-20ESect-2.7 P-21ESect-2.7 P-22ESect-2.7 P-23ESect-2.7 P-24ESect-2.7 P-25ESect-2.7 P-26ESect-2.7 P-27ESect-2.7 P-28ESect-2.7 P-29ESect-2.7 P-30ESect-2.7 P-31ESect-2.7 P-32ESect-2.7 P-33ESect-2.7 P-34ESect-2.7 P-35ESect-2.7 P-36ESect-2.8 P-1ESect-2.8 P-2ESect-2.8 P-3ESect-2.8 P-4ESect-2.8 P-5ESect-2.8 P-6ESect-2.8 P-7ESect-2.8 P-8ESect-2.8 P-9ESect-2.8 P-10ESect-2.8 P-11ESect-2.8 P-12ESect-2.8 P-13ESect-2.8 P-14ESect-2.8 P-15ESect-2.8 P-16ESect-2.8 P-17ESect-2.8 P-18ESect-2.8 P-19ESect-2.8 P-20ESect-2.8 P-21ESect-2.8 P-22ESect-2.8 P-23ESect-2.8 P-24ESect-2.8 P-25ESect-2.8 P-26ESect-2.8 P-27ESect-2.8 P-28ESect-2.8 P-29ESect-2.8 P-30ESect-2.8 P-31ESect-2.8 P-32ESect-2.8 P-33ESect-2.8 P-34ESect-2.8 P-35ESect-2.8 P-36ESect-2.8 P-37ESect-2.8 P-38ESect-2.8 P-39ESect-2.8 P-40ESect-2.8 P-41ESect-2.8 P-42ESect-2.8 P-43ESect-2.8 P-44ESect-2.8 P-45ESect-2.8 P-46ESect-2.8 P-47ESect-2.8 P-48ESect-2.8 P-49ESect-2.8 P-50ESect-2.9 P-1ESect-2.9 P-2ESect-2.9 P-3ESect-2.9 P-4ESect-2.9 P-5ESect-2.9 P-6ESect-2.9 P-7ESect-2.9 P-8ESect-2.9 P-9ESect-2.9 P-10ESect-2.9 P-11ESect-2.9 P-12ESect-2.9 P-13ESect-2.9 P-14ESect-2.9 P-15ESect-2.9 P-16ESect-2.9 P-17ESect-2.9 P-18ESect-2.9 P-19ESect-2.9 P-20ESect-2.9 P-21ESect-2.9 P-22ESect-2.9 P-23ESect-2.9 P-24ESect-2.9 P-25ESect-2.9 P-26ESect-2.9 P-27ESect-2.9 P-28ESect-2.9 P-29ESect-2.9 P-30ESect-2.9 P-31ESect-2.9 P-32ESect-2.9 P-33ESect-2.9 P-34ESect-2.9 P-35ESect-2.9 P-36ESect-2.9 P-37ESect-2.9 P-38ESect-2.9 P-39ESect-2.9 P-40ESect-2.9 P-41ESect-2.9 P-42ESect-2.R P-1CCSect-2.R P-2CCSect-2.R P-3CCSect-2.R P-4CCSect-2.R P-5CCSect-2.R P-6CCSect-2.R P-7CCSect-2.R P-8CCSect-2.R P-9CCSect-2.R P-10CCSect-2.R P-11CCSect-2.R P-12CCSect-2.R P-1TFQSect-2.R P-2TFQSect-2.R P-3TFQSect-2.R P-4TFQSect-2.R P-5TFQSect-2.R P-6TFQSect-2.R P-7TFQSect-2.R P-8TFQSect-2.R P-9TFQSect-2.R P-10TFQSect-2.R P-11TFQSect-2.R P-12TFQSect-2.R P-13TFQSect-2.R P-14TFQSect-2.R P-15TFQSect-2.R P-1ESect-2.R P-2ESect-2.R P-3ESect-2.R P-4ESect-2.R P-5ESect-2.R P-6ESect-2.R P-7ESect-2.R P-8ESect-2.R P-9ESect-2.R P-10ESect-2.R P-11ESect-2.R P-12ESect-2.R P-13ESect-2.R P-14ESect-2.R P-15ESect-2.R P-16ESect-2.R P-17ESect-2.R P-18ESect-2.R P-19ESect-2.R P-20ESect-2.R P-21ESect-2.R P-22ESect-2.R P-23ESect-2.R P-24ESect-2.R P-25ESect-2.R P-26ESect-2.R P-27ESect-2.R P-28ESect-2.R P-29ESect-2.R P-30ESect-2.R P-31ESect-2.R P-32ESect-2.R P-33ESect-2.R P-34ESect-2.R P-35ESect-2.R P-36ESect-2.R P-37ESect-2.R P-38ESect-2.R P-39ESect-2.R P-40ESect-2.R P-41ESect-2.R P-42ESect-2.R P-43ESect-2.R P-44ESect-2.R P-45ESect-2.R P-46ESect-2.R P-47ESect-2.R P-48ESect-2.R P-49ESect-2.R P-50ESect-2.R P-51ESect-2.R P-52ESect-2.R P-53ESect-2.R P-54ESect-2.R P-55ESect-2.R P-56ESect-2.R P-57ESect-2.R P-58ESect-2.R P-59ESect-2.R P-60ESect-2.R P-61ESect-2.R P-62ESect-2.R P-63ESect-2.R P-64ESect-2.R P-65ESect-2.R P-66ESect-2.R P-67ESect-2.R P-68ESect-2.R P-69ESect-2.R P-70ESect-2.R P-71ESect-2.R P-72ESect-2.R P-73ESect-2.R P-74ESect-2.R P-75ESect-2.R P-76ESect-2.R P-77ESect-2.R P-78ESect-2.R P-79ESect-2.R P-80ESect-2.R P-81ESect-2.R P-82ESect-2.R P-83ESect-2.R P-84ESect-2.R P-85ESect-2.R P-86ESect-2.R P-87ESect-2.R P-88ESect-2.R P-89ESect-2.R P-90ESect-2.R P-91ESect-2.R P-92ESect-2.P P-1PSect-2.P P-2PSect-2.P P-3PSect-2.P P-4PSect-2.P P-5PSect-2.P P-6PSect-2.P P-7PSect-2.P P-8PSect-2.P P-9PSect-2.P P-10PSect-2.P P-11PSect-2.P P-12PSect-2.P P-13PSect-2.P P-14PSect-2.P P-15PSect-2.P P-16PSect-2.P P-17PSect-2.P P-18PSect-2.P P-19PSect-2.P P-20PSect-2.P P-21PSect-2.P P-22PSect-2.P P-23PSect-2.P P-24PSect-2.P P-25PSect-2.P P-26PSect-2.P P-27PSect-2.P P-28P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Evaluate the expression sin Exercises 116. 33

Finite Mathematics and Applied Calculus (MindTap Course List)

Quotients Evaluate the quotient, and write the result in the form a + bi. 38. 11+i

Precalculus: Mathematics for Calculus (Standalone Book)

WORKER EFFICIENCY An efficiency study showed that the average worker at Delphi Electronics assembled cordless t...

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

In problems 13-16, Use notation to indicate which set is a subset of the other. 14.

Mathematical Applications for the Management, Life, and Social Sciences

Prove each identity. sin()cot()=cos

Trigonometry (MindTap Course List)

True or False: If , then converge absolutely.

Study Guide for Stewart's Multivariable Calculus, 8th

Finding an Indefinite Integral In Exercises 89-94, find the indefinite integral. 13+25x2dx

Calculus: Early Transcendental Functions (MindTap Course List)

Elimination of the parameter in x = 2t3/2, y = t2/3 gives: x4 = 16y9 16x4 = y4 x3 = 8y4 8x3 = y4

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Solve each equation. x3196x2+16x+1=0

College Algebra (MindTap Course List)