When https is used, does the web server request resources using SSL?

I have a website on Server A which users access via SSL (i.e. through an https URL). In order to respond to certain requests, Server A must make its own web requests to Server B.

Would A's requests to B be encrypted without a certificate bein开发者_JAVA百科g installed on B?

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That depends how A sends its requests to B. If A uses SSL/TLS to send the requests, they are encrypted, otherwise they are not. This is totally independent of whether or not A serves its own pages via HTTPS.