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I read that an ellipse had $2$ focal points. So, I thought if a circle had $2$ points that were simply infinitesimally close together wouldn't it be classified as an ellipse?

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    $\begingroup$ Yes, you can say that circle is a special case of an ellipse with coinciding semiaxis. $\endgroup$
    – Kaster
    Apr 25 '15 at 6:20
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    $\begingroup$ A circle is simply a degenerate ellipse, one in which the two focal points coincide. $\endgroup$ Apr 25 '15 at 6:21
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    $\begingroup$ I think to say that the foci are infinitesimally close is not a good way to say it. In circle, the foci are just the same point. $\endgroup$
    – Wojowu
    Apr 25 '15 at 6:26
  • $\begingroup$ Not sure if this should be asked in another question but can you draw an ellipse (that is not a circle) using a a pair of compasses? $\endgroup$
    – anonymous
    Apr 25 '15 at 6:43
  • $\begingroup$ @anonymous No. You can draw an ellipse using two pins and a string though. $\endgroup$
    – DRF
    Apr 25 '15 at 8:19
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Yes. A circle is a special case of an ellipse.

The equation of an ellipse centered at the origin $(0,0)$ is: $$\left(\frac xa \right)^2 + \left(\frac yb \right)^2=1$$

When $a=b=1$, this gives the equation of the unit circle: $x^2+y^2=1$.

In general, if $a=b=r$, you get the equation of a circle with radius $r$: $$x^2+y^2=r^2$$

Can you come up the equation of a circle not centered at $(0,0)$, but instead centered at $(h,k)$?

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Both the foci of a circle coincide and thus, its eccentricity is zero. So yes, it is an ellipse.
It is like that all squares are rectangles but all rectangles are not squares.
See this link- [the most intuitive link ever seen!] http://www.mathsisfun.com/geometry/eccentricity.html

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  • $\begingroup$ All rectangles are squares in SOME coordinate system :-) $\endgroup$ Apr 30 '15 at 10:53

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