Are mother and father burden to people who are busy with their lives? Were you a burden to them when they raised you to adulthood? Were you a burden to them when they fed and clothed and loved you unconditionally? I bet the majority of parents would say "absolutely not!"
Just because you have a busy life, it doesn't mean that you can ignore your parents or feel that it is a burden to have them a part of your life. I would give anything to have my parents around right now. Although neither was a perfect parent and both had many problems during their lives, I would have never considered them a burden.
My father died when I was eleven and in my small way, I helped take care of him during his three year battle with cancer. My mother passed away last year after a long difficult battle with COPD. My sisters and I often cared for her during her times of extreme pain and I was lucky enough to spend almost every moment with her during her last three weeks of life. Neither time did I feel as if my parents were "burdens." Instead, I felt it was a blessing to be able to spend any and all of this time with them....
No one should have a life that is too busy to consider their parents (or their children, for that matter) a burden!