Osculating Circles: Practice Page

Question 1: Is the curve (locally) inside or outside the osculating circle at a local maximum of curvature?

Question 2:Is the curve (locally) inside or outside the osculating circle at a local minimum of curvature?

Question 3: Is the curve (locally) inside or outside the osculating circle at a point that is not a vertex?

Question 4:Explain the relation between the osculating circle and the tangent line.

Question 5:What happens to the osculating circle near inflection points (where the curve changes from right turning to left turning, or concave to convex)? Why?

Question 6: Sketch the osculating circle at the points indicated on the figures below.

1. 2. 3. 4. 5.

Go to the concept page to read how to calculate curvature and radius of curvature.


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