   Chapter 13, Problem 13RQ

Chapter
Section
Textbook Problem

# Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.13. The osculating circle of a curve C at a point has the same tangent vector, normal vector, and curvature as C at that point.

To determine

Whether the osculating circle of a curve C at a point has the same tangent vector, normal vector, and curvature as C at that point is true or false.

Explanation
• The osculating circle at point P is the circle which lies in the osculating plane of C at P,
• It has the same tangent as C at P, which lies on the concave side of C,
• It shares the same normal, tangent and curvature at P,
• The radius of the circle is ρ

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