...

Code Block
<Context antiJARLocking="true" docBase="C:\Program Files\Tomcat\apache-tomcat-7.0.54\webapps\rator-selfcare-rest-api" path="" reloadable="true" source="org.eclipse.jst.jee.server:rator-selfcare-rest-api"/>

If the Tomcat's server.xml file had a <Context/> tag like the above, where the base path for the rator-selfcare-rest-api is set to the empty string, the project would be available at http://localhost:8080/rator-selfcare-rest-api/api/<SOME RESOURCE>.

 

When deploying from Eclipse, such entry might have been added automatically. Configuring the context in the server.xml seems to be discouraged by various online sources.  

...