How to project picture onto hair particles? Here I have a basic plane with hair particles (just for example) 
And here is something i want ,this black line, it should be visible when looking from angle in case when there is more particles on image up hair it’s too infrequent to be visible.

How can I do this? Also I would want to be able to move object and not change pattern while doing so.
This line is just an example I would like to add something different if this is even possible.
Add an image texture to hair-emitter-object and use object-coordinates. Then change the rotation (location and size if needed) of texture with mapping node to get the required result (In this example, for side projection, x or y = 90).