I want to make installer of my web application. For this I need to know where the Tomcat is installed (and either it is install or not) to drop the folder of my web application in the webapps folder of tomcat.
Depending on how they've installed it, you may have the CATALINA_HOME or CATALINA_BASE environment variables available.
Just knowing the location of the Tomcat installation, doesn't mean that you will know where to find the host directory. Tomcat can be configured in all kinds of ways. There is no guarantee that dropping a war file in the webapps directory will cause your app to be deployed unless you know that you're dealing with a default install.
I'm going to move this to the Apache Tomcat forum since it's more specific to Tomcat than to Servlets in general.