Comparing 2 GPS location data files to find if any location from one file is within a specified elliptical region of a location from another

I have 2 CSV files with GPS coordinates. I want to check if there are any locations in the first file which are inside a specified elliptical region surrounded by each location in the 2nd file. The major axis , minor axis and major axis bearing(angle) is given in the 2nd file for each location coordinates. For start I have plotted the points from both files in an ArcMap document where I can see red dots as first file locations and green dots as 2nd file locations.

For example if the coordinates of one location in 2nd file is 39.6145,-89.7823 (latitude(h), longitude(k)) and the major axis(a) 1200 and minor axis(b) 400 and bearing(A) 114 degree, then I want the list of the instances in first file which falls inside that region

N.B its is basically solving (x,y) in following equation, The image is basically the ellipse equation if you can't view it. 〖((x-h) cos⁡A+(y-k) sin⁡〖A)〗〗^2/a^2 +〖((x-h) sin⁡A-(y-k) cos⁡A)〗^2/b^2 ≤ 1

I am totally new in ArcGIS. I am also trying to do it in Python but want to know how to implement it in ArcGIS too. And both the files are pretty large, with millions of entries in both. So I would also like to know if it is too much time consuming in ArcGIS.

• Welcome to GIS SE. As a new user, please take the Tour, which emphasizes the importance of asking one question per question. You have several questions here, and some confusion in trying to differentiate ArcGIS from Python (most ArcGIS scripting is in Python). Since ArcPy has the functions you need to generate ellipses from geodetic parameters, I suggest you start there. I process millions of rows against tens of millions of rows frequently from ArcPy; there are some gotchas with inefficient/unindexed queries, but it runs just fine for simple operations (such as selecting by polygon). – Vince Sep 20 at 20:33
• thanks for your comment. I thought I could use Arcgis to get the required points as I am dealing with coordinates and map locations. thanks for suggesting ArcPy. I will look into it. I am basically new in learning the programming. i was trying to do it in python just solving the equation but its taking way too long. when i saw a friend plotting points in Arcgis, I hoped there would be some way to do it more efficiently in Arcgis. – Tanzin Farhat Sep 20 at 20:50
• Using ArcGIS (or any GIS) to plot points is like using the case of a 400-tool Leatherman to poke holes in sand -- There's far more capability than you're using. Solving that equation on a spheroid requires iterative means for each vertex except the last one (since that's the same as the first). Much better to use a tool with a pre-defined function. – Vince Sep 21 at 2:18