Thanks for the help.
Actually, the "Private" button is on the lower left corner of the screen. I called Apple support and they said I could not open my Yahoo email because my email was "corrupted". However, after I gave them access to the account they said they could fix the problem for a "one time" fee of $129.99. When I said no, they offered to drop the fee to $100. I said no thanks, and good bye.
I then called the local Apple retail store and the rep. explained exactly what you suggested on this forum. My email had locked up because I tried it so many times so I called the Yahoo folks. Their rep. set me up with a new password and it worked. Interestingly the Yahoo rep. knew about the Safari "private browsing". Seems like Apple support is either "uninformed" or wants to charge people for service.