# Questions tagged [osculating-circle]

For questions about osculating-circles, Descartes Theorem, Radius of Curvature, and evolutes.

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### Showing that a circle is an osculating circle of a unit-speed curve

Let $\alpha : I\to\mathbb{R}^2$ be a smooth plane curve parametrized by arc length, and assume that $0\in I$. A circle with radius $r$ centred at $p$ is called the osculating circle of $\alpha$ at $0$ ...
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### Find the amplitude of the oscillation of the particle.

The displacement of a particle varies according to $x=3(\cos t +\sin t)$. Then find the amplitude of the oscillation of the particle. Can someone kindly explain the concept of amplitude and ...
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### How can I find a point where an osculating circle goes through a certain point?

Given a point $P = (x_P, y_P)$ and a function $f(x)$, how can I find the set of all points $Q\in f$ such that the periphery of the osculating circle to $f$ in $Q$ goes through $P$? Is there a curve ...
1answer
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### Osculating circles intersecting a given point

Well, the problem is a question in Montiel's book. How to prove that a planar curve $\alpha$ such that all osculating circles intersects a given point is actually a circle (or a part of it)? I've ...