Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Q18P (page 407)

Find the family of orthogonal trajectories of the circles (x-h)2+y2=h2. (See the instructions above Problem 2.31.)

Short Answer

Expert verified

Answer

The family of orthogonal trajectories of the circles:

Step by step solution

01

Given information

The given equation of the circle isx-h2+y2=h2.

02

Standard equation of a circle

The standard equation of a circle is (x-h)2+(y-k)2=r2

Here, (h,k)is the center of the circle and r is the radius of the circle.

03

The orthogonal trajectories of the circle

The given equation of the circle is,

x-h2+y2=h2

The standard equation of a circle is

x-h2+y-k2=r2............i

where h,k is the center of the circle and r is the radius of the circle.

Now, compare equation (1) with the standard form of equation, which indicates that

h,0is the center of the circle and h is the radius of the circle.

Therefore, it can be said that the equation (1) shows a family of circles with center h,0and radius h. The value of h varies from ∞to ∞.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Using (3.9), find the general solution of each of the following differential equations. Compare a computer solution and, if necessary, reconcile it with yours. Hint: See comments just after (3.9), and Example .

y+y/x2+1=1/(x+x2+1)

By using Laplace transforms, solve the following differential equations subject to the given initial conditions.

y"+y=sint,3t=0,y'0=-12,

Use L28 to find the Laplace transform of

f(t)={sin(t-π/2,t>π/20,t<π/2

Find the transform of

f(t)={sin(x-vt),t>x/v0,t<x/v

Where xand vare constants.

The speed of a particle on the x axis, x≥0, is always numerically equal to the square root of its displacement x. If x=0when t=0, find x as a function of t. Show that the given conditions are satisfied if the particle remains at the origin for any arbitrary length of time t0and then moves away; find x for t>t0for this case.
See all solutions

Recommended explanations on Physics Textbooks

Radiation

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Electric Charge Field and Potential

Read Explanation

Energy Physics

Read Explanation

Medical Physics

Read Explanation

Work Energy and Power

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.

Sign-up for free