We only have family out of state, so if we're lucky, two or three will come to the actual recital, and our tickets are $10 each. So, we pay for them since they have to travel 4 hours to get here to begin with.
Each studio is different - some offer a minimum number of tickets to the family, then they have to buy the rest they need, some studios don't do a true "recital" and it's more like a talent show with no charge. Depends on where you're at. Many of your guests may not know that you're paying for the tickets for them to attend. I'd just let them know when you invite them that there is a cost of $13 each - maybe you could offer to pay the first $5.00 of each ticket if you're unable to pick up the entire tab this year.
My daughter has been dancing since she was 4, that was 7 years ago! Lots of recitals and performances! She is now on a production team and a competition team in addition to her classes at her studio, so she also performs at several other events throughout the year and so we can film her at various events and e-mail the footage to our out of state family. Plus we buy the $50 DVD that is offered from the studio at the end of the year which we can then send to different people to see if they want. It's a great DVD because the numbers are indexed and you can select the individual ones to watch without watching all 4 hours of it!
This year she will perform a total of two days of competitions, she's already performed at the township's annual silent auction event, is scheduled for all 5 of the studio's recitals, which, of course, includes 5 dress rehearsals!, and then will be at the Relay for Life event at Heritage Park in May. She was also invited to perform on a Royal Carribean Cruise line in the summer, however, we have to pass on that one since my niece is getting married the same weekend and she'll be in the wedding in California.
So plenty of opportunity for our family to see her without paying for tickets.