Question

Find an equation of the graph that consists of all points $(x, y)$ having the given distance from the origin. (For a review of the Distance Formula, see Appendix D.) The distance from the origin is $K(K \neq 1)$ times the distance from $(2,0)$.

Name: Problem 86, Chapter 0: Calculus
Uploaded: 2021-09-25T10:27:47-08:00
Duration: 1 min 40 s
Channel: Yujie Wang
Description: Find an equation of the graph that consists of all points (x, y) having the given distance from the origin. (For a review of the Distance Formula, see Appendix D.) The distance from the origin is K(K ≠1) times the distance from (2,0).

   Find an equation of the graph that consists of all points $(x, y)$ having the given distance from the origin. (For a review of the Distance Formula, see Appendix D.)
The distance from the origin is $K(K \neq 1)$ times the distance from $(2,0)$.

Calculus

Ron Larson, Robert… 8th Edition

Chapter 0, Problem 86

Instant Answer

Solved by Expert Yujie Wang

09/25/2021

Step 1

Using the distance formula, we get $\sqrt{x^2 + y^2}$. Show more…

Show all steps

Thanks for your feedback!

Find an equation of the graph that consists of all points $(x, y)$ having the given distance from the origin. (For a review of the Distance Formula, see Appendix D.) The distance from the origin is $K(K \neq 1)$ times the distance from $(2,0)$.

Play audio

Feedback

Yujie Wang and 94 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Distance Formula

The distance formula computes the Euclidean distance between two points in the coordinate plane using the square root of the sum of the squares of the differences in their coordinates. It is essential for translating geometric distance conditions into algebraic equations.

Locus Defined by Distance Ratios

When a set of points is described by a condition that their distances to two fixed points have a constant ratio, this condition defines a locus. Understanding how to set up and manipulate this distance condition is fundamental to finding the corresponding equation.

Apollonius Circle

An Apollonius circle is the set of all points for which the ratio of distances to two fixed points is constant (with the ratio not equal to one). Recognizing this concept helps in rewriting the distance condition as a standard circle equation by applying the distance formula and algebraic techniques.

Please give Ace some feedback