FWIMBW: I came to the Java 6 back-up, Java 8.25 update discussion because Adobe Photoshop CS5.1 failed to open after upgrading to Yosemite.
I have a bag full of Adobe products. Of those I tested, only Photoshop SC5.1 was a deader---PS Elements 12, Premier Elements 12, Lightroom 5, Bridge CS5.1 Dreamweaver CS5.5, Audition CS5.5, Illustrator CS5, and Acrobat X Pro opened fine. Like others posting here, I got a warning after installing Yosemite that a Java fix was needed. I scurried around and got a link at Apple Support to a patch. Instructions were cryptic and not very useful.
1. I downloaded and installed Apple's recommended back-up patch (Java for OS X 2014-001). Photoshop would not open. Got this cryptic garbage:
2. I went to Oracle, downloaded and installed the JRE 8 v 25 update--not the developer version, and not the JRE 7 Apple seems to prefer. I verified that this version existed on my computer using the Oracle verify Java utility in the two browsers I routinely use. Alas, for me Chrome has become a deader (32-bit only; works with Java 6 only), but offered some plausible information and links about how to undo Java updates beyond 6. Photoshop still would not open. Same report.
3. Following suggestions posted here, I used Terminal very judiciously to try to find things I did not at all understand in various Library folders. Got quite bummed out by seeming differences between Yosemite and now-dead earlier OS versions, as in no Java panel in 10.10 System Preferences or the Utilities folder within Applications. I logged out and restarted a number of times. Photoshop still would not open. Same report.
4. Dug around, found my CS Design Premium DVD, and reinstalled Photoshop CS5 in a new folder, leaving the version that repeatedly exited itself in place. Photoshop CS5 now opens and works. So (apparently) do Safari and Firefox.
5. Now trying to update from Photoshop version 12.0.4 to 12.1 (supposedly a freebie) and resetting pointers to a a few dozen third-party plug-ins for Photoshop. And to avoid Adobe Application Manager updates that either don't install, or are older than what I already have.