How to check if page exists in powershell?

I write the powershell script below to check if a webpart exists on some page on all mysites. I got an exception on the root site collection of the mysite webapplication because the page does not exists.

How to avoid this exception? I would like to check for example if the page exists but it looks like it dont work. I check already if the variable $page is not null.

Add-PSSnapin Microsoft.SharePoint.PowerShell -EA silentlycontinue

$webAppUrl = "http://MyWebApplication.com"
$spWebApp = Get-SPWebApplication $webAppUrl

foreach($SpSite in $spWebApp.Sites)         
{  
        $resultsUrl = $SpSite.Url +"/Social/Sites.aspx"
        $page = $SpSite.RootWeb.GetFile($resultsUrl);

        if($page -ne $null)
        {
            # Get the web part manager for the page
            $webPartManager = $SpSite.RootWeb.GetLimitedWebPartManager($resultsUrl, [System.Web.UI.WebControls.WebParts.PersonalizationScope]::Shared)

            # And pull the web part we want to work on
            $webpart = $webpartmanager.WebParts | ? { $_.GetType().Name -eq 'MyCustomWebpart' }
            if($webpart -ne $null)
            {
                "Found webpart '" + $webpart.Title + "' " + "on page $resultsUrl"
            }
        }

    $SpSite.RootWeb.Dispose();
    $SpSite.Dispose();
}