So basically i am task to ask user for points to draw straight line and curve. How do i write a program prompting them to draw straight line and curve using homogenous coordinates?
There’s a lot more to a problem like this than you might expect, so we need a lot more information first. I can see two separate sub-problems: getting the input, and drawing the curve. I assume you are asking about both.
How do you want to get the input? For example, are you trying to make some graphical dialog box pop up to ask for them, or do you just want to use the normal input in the terminal? Either way, the hard part will be deciding the rules for exactly what the user types, and how to interpret that as program data. Input from the user is a string, and you need to decide what parts of the string have what meaning (parse the string). Maybe these ideas will be enough to get you started:
If you want to get multiple coordinates all at once, I guess you will be looking at some nested data (like a tuple of tuples). An approach like ast.literal_eval (should be covered in one of those Q&As) will be powerful enough for that, but you will need to verify the structure of the data afterward (because it is much more powerful, and could interpret input that isn’t what you want).
For drawing the curve, do you understand how the math works, or is this just about how to tell the Turtle library to draw things? Do you want to use homogeneous coordinates because you expect it to make the drawing problem simpler, or is it just your requirement for how the code should work?