Finding specific coordinates in geotiff bigtiff image

In the preprocessed image with subsetted, orbit file applied and terrain corrected with 50m pixel spacing.
I am trying to find which pixels(row,column) contains desired point coordinates.
Can I just use ratio of (target points longitude - leftmost points longitude)/( full longitude length of the image) as linear 1 to 1 scale or does curvature has any affect.
And how should I account for the angle created after geocoding. [ The image apperas to be tilted and remaining pixels surrounding image becomes 0]
And lastly the coordinates written in geotiff-bigtiff file is not the coordinates of all image( including filler 0’s added), but real coordinates of the image; is this true ?

I am really open for your guidance