# Working with orthogonal trajectories

Not what you're looking for?

(a)Find the orthogonal trajectories of the family of curves defined by

2cy + x2 = c2, c>0

State the differential equation of the orthogonal family, and show your steps in obtaining a solution.

(b) On the same set of "square" axes, plot at least five members of each of the given family and your family of orthogonal solutions.

(c) Identify one point of intersection, and approximate the coordinates of the point. Determine the slope of each curve at the point of intersection, and verify that the tangents are indeed perpendicular.

NOTE: So far, I've done implicit differentiation, and gotten 2cdy/dx + 2x = 0. Then I solved for c (from the original equation) by using the quadratic formula. But when I plug c back in and try to solve the differential equation (I've been getting a homogeneous differential equation and substitute x=vy), it doesn't seem to turn out right. Either the D.E. is too hard to integrate; or I can't get the tangents to be perpendicular in the end.

##### Purchase this Solution

##### Solution Summary

The orthogonal trajectories for differential equations are provided. Clear explanations and all mathematical steps are provided.

##### Solution Preview

Please view the attached document..

2cy + x2 = c2, c>0

Solution

The level curves constitute a family of curves, one for each value of the constant, and this family can be described by a single differential equation. We find the DE by eliminating the constant. This is ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.