I've bought a VPS witch has 2 public IP addresses assigned to it.
I want to configure Apache so I can have two different sites (in separated directories), each one available from a different public IP.
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I hope you need to configure Apache for hosting two websites in two different IP address. This is whats called IP based virtual hosting. for this you need configure the both ipaddress in apache2.conf file with Listen Directive.
After restarting you can see that apache is listening on both IPs by applying netstat -ntlp.