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Tested on Proj 6.2.0.
echo -120.234501 30.234501 0 | ./src/.libs/proj +proj=aeqd +a=6371008.771415 +b=6371008.771415 +lat_0=30.2345 +lon_0=-120.2345
In the first command we have a==b which seems to go through the spherical support in aeqd.cpp. In the second command, b is an epsilon smaller which triggers the ellipsoidal code path.
I would expect the first command to return something similar to the second one.