Here are a few options you can try..
You can't just close your answers account it is a part of your yahoo account.
If you no longer want to use your Answers account, you can only "mothball" it:
* remove your Contacts
* remove your avatar
* change the name to ? or a few dots
* turn off all notifications and emails
* set all settings to private/don't share
* then just stop using it
None of this will stop your questions and answers being visible, either through a Yahoo or Google search.
You will keep getting points if old answers get voted as BA.
You will keep getting notices of this (or of violations, if old content is reported) but you can set up your mail to direct these to the trash folder.
If you want to close your Yahoo account
Before closing your account, please understand:
•A closed account cannot be reactivated – While you can always sign up for a new account, closing an account will remove and delete it from the Yahoo! network.
•You cannot just delete a single Yahoo! product. You will lose access, data, and settings for all Yahoo! ID associated with the closed account – This includes all messages in Yahoo! Mail and any personalization made in Yahoo! Mobile, and any other area of Yahoo! which can only be accessed with your Yahoo! ID and password.
If after this if you still want to close your Yahoo account Visit the Account Termination page.
http://help.yahoo.com/kb/index?page=content&id=SLN46&actp=search&viewlocale=en_US&searchid=1341752971085&locale=en_US&y=PROD_ACCTn