Equation of oscillating circle

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Homework Help Overview

The discussion revolves around finding the equation of an osculating circle related to a curve, with a focus on understanding the radius of curvature and its application in determining the circle's equation.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to find the equation of the osculating circle after calculating the radius of curvature but expresses uncertainty about the next steps. Some participants question the differentiation process and suggest using the normal vector to aid in finding the circle's center.

Discussion Status

Participants are actively engaging in clarifying the steps necessary to find the equation of the osculating circle. There is an acknowledgment of an error in the original poster's differentiation, and guidance has been offered regarding the relationship between the radius of curvature and the normal vector.

Contextual Notes

The original poster has indicated a lack of confidence in their mathematical skills and is seeking verification of their calculations alongside guidance on the next steps in the problem-solving process.

sakkid95
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http://gyazo.com/bc7f6da4d4c4aca300bb5efb2410fc8d.png


The problem, and my solution are in the image. I need help on finding the equation of the osculating circle, I found radius but I don't know where to go from there. Also if you could just check if my math seems correct that would help me too, but my main problem is how I find the eqn for the circle... thanks in advance
 
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You made a mistake differentiating t3.
You have the radius of curvature; from the tangent you can find the normal vector.
 
Yea I noticed the error, I'm working on fixing it now. Can you elaborate more on how to find the radius? I'm not very good at this stuff..
 
sakkid95 said:
Yea I noticed the error, I'm working on fixing it now. Can you elaborate more on how to find the radius? I'm not very good at this stuff..

You said you had the radius. If so, all you need is a line the circle's centre must lie on. The normal to the curve is that line.
 

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