There's a_____(write)desk.

writing

writing desk 写字台

writting.桌子不可能是被写的.只有句子,书本是被写的.the written book.
writing本身可为写作的意思,这里表DESK的性质功能.DESK的功能是用来帮助"写"的.

楼上正解 补充一下 writing在这里是现在分词做定语 相当于形容词~

There's a writing desk.