Instagram is one of the most widely used photo application which allows you to share photo or video to social networking sites such as Facebook, Twitter, Flickr, Foursquare, and much more. If you share photo or video using Instagram to social networking site with private profile, then the photo will be visible on that site and the permalink will be active. So who has access to its direct link, they can view the photo. If you share a photo to social networking site, then it doesn't mean that the photo will be visible in Instagram account. Your account will still appear private to those who are not approved followers.