Wherever the projected 'cone' would touch the earth a standard parallel is drawn. In this projection the farther away from the standard parallel you get the more distortion occurs. Conic projections are useful in portraying the middle latitudes in an east to west fashion. The Lambert Equal Area projection assumes that there is a plane touching the earth at a single point. The closer to the center point you get the more accurate this type of map will be.
Equal area means showing landmasses in their correct proportion.
The Lambert Equal Area projection is used quite frequently for polar projections. The Miller Cylindrical projection is an adapted Mercator projection based on the suggestions of O. M. Miller. It is used to quieten the high latitude distortions of the Mercator maps. It is neither conformal or equal area, but it does reduce the extreme exaggeration of size shown in the higher latitudes of the Mercator projections. This map is very handy for showing the entire earth in a rectangular format.