Private key:
openssl ecparam -name secp256k1 -genkey -noout -out sample-priv-key.pem
Public key (from private key):
openssl ec -in sample-priv-key.pem -pubout > sample-pub-key.pem
Read file info
openssl ec -text -in sample-priv-key.pem
(ecparam is for Eliptic Curves params)