# Tagged Questions

For questions conserning circles. A circle is a curve composed of points in a plane that are at a fixed distance from a fixed point.

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### Why Circle is traced counterclockwise and ellipse is traced clock wise?

In the Lecture 32: Polar Coordinates,professor traces the circle counterclockwise, but traces the ellipse clockwise. "Which was this one here. And first we noted that this does parameterize, as we ...
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### What happens when $r \to \infty$? Will it be a line? (partial circle)

Let $a$ be a arc of particle circles, which is constant. What happens when $r \to \infty$? Will it be a line? Radius of partial circle : $r$, Arc of partial circle : $a$ and constant, For $r=r_0$ ...
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### Determining Locations of Circles to Optimally Cover a Polygon

I want to completely cover a region on a map(Continental US)/polygon with circles of a certain radius. Is there a way to determine the best locations and how many circles would be needed to completely ...
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### How to calculate $\Delta$ in conic sections?

When learning conic section I learnt about $\Delta$. For any conic in general form : $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ Here $\Delta=abc +2fgh - af^2 - bg^2 -ch^2$ The conic is said to be ...
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### How to determine if the implicit curve is closed?

Let the implicit equation $$F(x,y)=0, \quad (x,y)\in\mathbb{R}^2$$ defines a curve $\gamma$. The question is what properties must have the function $F$, s.t. the curve $\gamma$ be topologically ...
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### Radius of inner circles given radius of outer circle and number of inner circles in circular fractal

I am trying to create a circular fractal in which each circle is composed by a given number $n$ of smaller circles. It would look something like this for $n = 8$: However, I don't know how to ...
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