Search bar in right click menu

OK, so I realized something today. Firefox has a wonky method if checked in settings where you can have a search bar in the middle of your google homepage
as normal. If i click in the search box to make it active and start typing NO text appears there, it shows in the TOP url/address bar instead. Ok, well then if in settings I choose NOT to show a search bar on my HOME page, then my entire page is just blank so basically a entire blank screen, Wasted space then, and I have to travel all the way up to the url bar to be able to search anything. DUMB, is there already this out there, or can one of you developers make it so whether I bring up my right click menu either in firefox screen or say just right clicking on my desktop can someone make a search bar right on the top of it(with focus for typing) so when i do right click i can just type what i want to search for and hit enter???