   Chapter 3.R, Problem 40E

Chapter
Section
Textbook Problem

# Find the point on the hyperbola x y = 8 that is closest to the point (3, 0).

To determine

To find:

The point on hyperbola xy=8 which is closest to the point (3, 0)

Explanation

1) Concept:

To find the distance between two points, use the distance formula.

2) Formula:

i) The distance formula dx,y=x2-x12+y2-y12

ii) Power rule for xn is given by ddxxn=nxn-1

3) Given:

xy=8, the equation of hyperbola.

4) Calculation:

The equation of hyperbola is xy=8,

Solve for y from this.

xy=8

y=8x

so every point on this hyperbola is of the form x, 8x

Let A=3, 0 and B=x, 8x

Now the distance between point (3, 0) to this point of hyperbola x, 8x can be calculated by using the distance formula

dA,B=x-32+8x-02

dA,B=x2-6

### 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

#### In Exercises 73-80, find the indicated limits, if they exist. 73. limx3x+2x5

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

#### Evaluate: 12x21xdx. a) 322 b) 2+21 c) 4+2 d) 14

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

#### The unit vector in the direction of is:

Study Guide for Stewart's Multivariable Calculus, 8th

#### Explain how inter-rater reliability is established.

Research Methods for the Behavioral Sciences (MindTap Course List)

#### Simplify. 25a2b(2a2ba+b2)

Mathematics For Machine Technology 