Finding equation of osculating circles of ellipse

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digipony
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Homework Statement


Find the equations of the osculating circles of the ellipse 9x^2 + 4y^2 =36 at the points (2,0) and (0,3)


Homework Equations





The Attempt at a Solution


I honestly have no idea what to do here. This problem is in the chapter relating to curvature and arc length, as well as unit tangent/normal/binormal vectors for vector functions, but I do not see the relation of these topics to this problem. For some reason I have the idea of parametric equations come to mind. Could someone please point me in the right direction?
 

Answers and Replies

  • #2
LCKurtz
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Homework Statement


Find the equations of the osculating circles of the ellipse 9x^2 + 4y^2 =36 at the points (2,0) and (0,3)


Homework Equations





The Attempt at a Solution


I honestly have no idea what to do here. This problem is in the chapter relating to curvature and arc length, as well as unit tangent/normal/binormal vectors for vector functions, but I do not see the relation of these topics to this problem. For some reason I have the idea of parametric equations come to mind. Could someone please point me in the right direction?

Do you know how to calculate the curvature at (0,3)? The osculating circle has the same radius as the radius of curvature of the ellipse and is tangent to the ellipse on the concave side.
 

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