Look into the canvas object.
But be forewarned that it's an HTML5 object, so even it is not universal. But it may be as close as you come.
If you don't need the drawing to be "real time" (that is, if you simply want to offer up an image that is already drawn), then you could use server-side code to produce an image (e.g., a JPG or PNG file) that you then simply display on the page. That will work with any browser, since it has nothing to do with the browser, per se.
How you will produce such an image will depend on what server technology you are using. I know how to do it with ASP and ASP.NET code, for example. There are PHP gurus here who could tell you how to do it with PHP code.
An optimist sees the glass as half full.
A pessimist sees the glass as half empty.
A realist drinks it no matter how much there is.