Eomonth conditional formating

[JoeNichols]

I am trying to add conditional formatting using end of month.

What I am hoping to have is this:
Enter a date in "A1"
Next "A2" has formula "=EOMONTH(A1,36)"

I would like to have three conditional formats showing
"Green" if today's date is in the preceding calendar month or earlier than "A2"
"Yellow" if today's date is within the calendar month of "A2"
"Red" if today's date is after the calendar month of "A2"

I would also like to have this shown on a different sheet in the same workbook if possible.

Thanks.

 

[JoeNichols]

Also, is it possible to have the "A2" cell
(Next "A2" has formula "=EOMONTH(A1,36)")
only show the result of the formula if a date is typed in "A1", otherwise be shown as blank?