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I have a number of locations (latitudes and longitudes) in my data. If each location is a member of ellipse, I want to find the centre (in cartesian coordinates) of the ellipse. The data looks like:

            longitude  latitude
location 1  -118.8267  33.73430
location 2  -115.9665  33.25514
location 3  -117.2978  34.18589
location 4  -117.2962. 34.18449
location 5  -117.1625  34.00642

Please note that I do not have any information regarding the major axis length and minor axis length of the ellipses.

I want to know, is there any way in R programming language by which I can find the cartesian coordinates of the centre of the ellipses the locations belong to? And how to find the major and minor axis lengths as well?

Geo

**EDIT**:

In my question, each location will be a member of a "different" ellipse. Now, an ellipse consists of at least 3 points. In my analysis,I will first classify the locations into several different groups according to some model criteria. Then there will be several different "ellipses". Each location point will be a member of one of these classified ellipse.

Geotas
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  • Have you seen [this post](http://lastresortsoftware.blogspot.com.au/2012/09/fitting-ellipse-to-point-data.html); or [this post here on SO](https://stackoverflow.com/questions/46160044/fitting-data-points-to-an-ellipse-with-its-center-at-the-origin-using-r)? This seems to be a duplicate. – Maurits Evers May 13 '18 at 06:12
  • Hi @MauritsEvers, no I have not seen this link before. Thank you so much! But I think in the first link they are considering that all the data points are a member of one ellipse. In my case, this is different. – Geotas May 13 '18 at 06:22
  • So when you said every *"location is a member of ellipse"*, do you mean *different* ellipses? An ellipse is uniquely determined by at leat 3 points. In other words, you can't estimate the parameters of an ellipse with anything less than 3 points. – Maurits Evers May 13 '18 at 06:27
  • Hi @MauritsEvers; no. Basically not all of them are members of different ellipse. First of all, I will classify them according to some model criteria so that there are several different groups. Each group will have more than 3 events. So the ellipses will have at least 3 points. – Geotas May 13 '18 at 06:32
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    *How* do you classify which points below to which ellipse? *What* are these model criteria. I'm sorry but this is not clear at all. You need to provide more information. Perhaps it would help if you were to provide a reproducible minimal example: Show sample data and then the expected output (the ellipses) based on the data. – Maurits Evers May 13 '18 at 06:45

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