Specifically finding points along the circle. If possible without converting into Northing/Easting beforehand. I'm looking for the fastest possible way to calculate points in Latitude/Longitude in a circle around a point on the Earth ellipsoid. I've seen ways to figure out a circle of a sphere, however not while using Latitude and Longitude angles directly and not on an ellipsoid.
I have done this before using forward azimuths, here is a link that has descriptions and algorithms that may be helpful:
A forward azimuth calculates a new point that is a specified distance and compass bearing from a starting point. The basic idea is that you have a point in Lat/Lon and you calculate a series of forward azimuths with a range of angles. The number of calculations depends on how many vertices you want in your circle, normally I would use 360 so I get one vertex for every degree of the circle which should look good for most applications.