Telling the Truth vs. Protecting a Family's Image

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I was recently reminded of this dilemma that we must all experience at one time or another. In my case, I had to choose between lying to a good friend about my reluctance to hang out with her or tell her the truth -- that my parents no longer permitted me to do so. The former makes me seem disinterested in being her friend, which over time can ruin our relationship. It also satisfies my parents. However, the latter shows that I trust her with such private information, but it also makes my family seem close-minded. When is it necessary to maintain the family image and when is it alright to tell the truth, even if it does not put your family in the best light? Where do you draw the line?