The answer to this question is going to vary from state to state within the United States. This is especially true on the issue of abortion.
In general, parents are allowed unlimited access to medical information about their minor children. However, there are some exceptions to this rule. According to the federal law, the main exception that applies to your question is that parents may not be informed about children's medical information
When the minor is the one who consents to care and the consent of the parent is not required under State or other applicable law
So, as you can see, that could be very different in different states. This is especially true of abortions since different states have different rules about parental notification.