If your Mac is running OS X, it can both read and write to your Win NTFS drive. But it is not setup to allow that function by default.
This article at CNet explains how to enable your Mac to use your former Windows backup disc: http://www.cnet.com/news/how-to-manually-enable-ntfs-read-and-write-in-os-x/
If you are not comfortable making the systems file edits mentioned in the article, simply purchase the third-party drivers mentioned in the first paragraph of the same article.
Cheers.
