## Related questions with answers

Question

Consider the family of circles

$x ^ { 2 } + y ^ { 2 } = 2 c x.$

Show that the differential equation for determining the family of orthogonal trajectories is

$\frac { d y } { d x } = \frac { 2 x y } { x ^ { 2 } - y ^ { 2 } }.$

Solution

VerifiedStep 1

1 of 6$x^2+y^2=2cx\rightarrow 2x+2y\dfrac{dy}{dx}=2c$

We are given the original family of curves and their orthogonal trajectories. The goal is to find the orthogonal trajectory of the given equation and show that it is the same as the given orthogonal trajectory. So first, take the given equation and derive implicitly with respect to x.

## Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Recommended textbook solutions

#### Differential Equations and Linear Algebra

2nd Edition•ISBN: 9780131860612 (4 more)Beverly H. West, Hall, Jean Marie McDill, Jerry Farlow2,405 solutions

#### Differential Equations and Linear Algebra

4th Edition•ISBN: 9780134497181 (1 more)C. Henry Edwards, David Calvis, David E. Penney2,376 solutions

#### Differential Equations and Linear Algebra

3rd Edition•ISBN: 9780136054252 (4 more)Bruce H. Edwards, Penney2,317 solutions

#### Differential Equations and Linear Algebra

4th Edition•ISBN: 9780321964670Scott A. Annin, Stephen W. Goode3,457 solutions

## More related questions

1/4

1/7