how can i recover my mac by installing OS X when it does not give me a disc to choose where to install on

That may be because the disk needs to be reformatted or the disk has failed. If you have a functioning Recovery HD, then do the following:

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1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility from the main menu and click on the Continue button.
3. After Disk Utilityloads select the volume (this is the indented entry, usually Macintosh HD) from the side list. Click on the Erase button in Disk Utility's toolbar.
4. Set the Format type to Mac OS Extended (Journaled.) Click on the Apply button
5. When the process has completed quit Disk Utility and return to the Utility Menu.
6. Select Install OS X and click on the Continue button. 

If your drive does not appear in Disk Utility, then it has failed.