Why can't websites access JRE in Yosemite? Please see the attached image which shows an error/information message I am seeing regularly since upgrading to Yosemite. I don't know which website is asking for Java, as there is a different site showing in Safari each time I see it, but I do know that I am using the latest version of JRE so it's not clear why this message is being shown.

Can someone please advise me the best way to check what process is generating this, and how I can fix it?
As suggested by Moto_Nomad, this appears to have been caused by the Facebook Video Chat plugin requesting Java Runtime Environment. I needed to undertake the following steps to locate and disable this process.

Launch Terminal, and type the command launchctl list | grep facebook

This results in something like the following:

-   1   com.facebook.videochat.&lt;yourname&gt;.updater
-   0   com.apple.facebook.xpc


Where &lt;yourname&gt; is your Facebook id. To delete the process, type the following command:

launchctl remove com.facebook.videochat.&lt;yourname&gt;.updater

Remember to replace &lt;yourname&gt; with the Facebook ID returned in the first step. To check the command has worked, type launchctl list | grep facebook again. This time you should see the following:

-   0   com.apple.facebook.xpc


Having done this myself I can confirm that the dialog shown in the question is no longer appearing.