This is a site administration question not a developer question.
Instead of hiding the page you can have different content shown when authenticated and not authenticated.
Add 2 Html modules to the page and in the settigns of one check Hide From Authenticated - this will show when the user is not signed in.
on the second one marke it hide from anonymous.
Note however these are cosmetic settings not security settings. You can also specify which roles can view it if you want to secure the content.
Hope it helps,
Joe