Enabling mod_rewrite in Apache:

LoadModule rewrite_module modules/mod_rewrite.so

mod_rewrite:

RewriteEngine On
RewriteBase /
RewriteRule ^api/(.*)$ http://127.0.0.1:8080/api/$1 [P]
LoadModule rewrite_module modules/mod_rewrite.so
LoadModule proxy_module modules/mod_proxy.so
LoadModule proxy_http_module modules/mod_proxy_http.so
Listen 80
NameVirtualHost 127.0.0.1
<VirtualHost 127.0.0.1>
   ServerName localhost
   DocumentRoot /var/www
</VirtualHost>