I wouldn't count on it. URLs use "real" slashes, not backslashes, so HTTP:\\10.226.236.12:8080\\EmergencyImagePush\Firstpage.jsp will only work on web clients that accept invalid URL syntax and compensate for it.
I get the impression that you don't understand what a URL really it (hint: it's
not a filename path, and it's made of of several distinct components). It would be a good idea to learn about URLs and URIs, since the concept is central to the Internet - and not just for the World Wide Web part of it.
Having said that, a URL in the form of "http://image" (note the slashes!) only works if your hostname is "image". This is actually an incomplete URL and (again)
you should expect that it won't work reliably except for web clients that compensate for its deficiencies.
So you need to learn about:
URLs and URIs
hostnames
domain names
well-known ports
domain name resolution and Domain Name Services (DNS)
Proxying and forwarding
Common client practices for resolving incomplete URLs
After that,
then you'll be in a position to configure
Tomcat properly.
Some people, when well-known sources tell them that fire will burn them, don't put their hands in the fire.
Some people, being skeptical, will put their hands in the fire, get burned, and learn not to put their hands in the fire.
And some people, believing that they know better than well-known sources, will claim it's a lie, put their hands in the fire, and continue to scream it's a lie even as their hands burn down to charred stumps.