Telling your parents shouldn't be such a big deal. You are almost an adult. You should accept some responsibilty as an adult.
So, why do you not want to fight the ticket? You were almost certainly cited for VC22350. This has got to be one of the easiest tickets to beat. 22350 states:
22350. No person shall drive a vehicle upon a highway at a speed
greater than is reasonable or prudent having due regard for weather,
visibility, the traffic on, and the surface and width of, the
highway, and in no event at a speed which endangers the safety of
persons or property.
Notice there is nothing there that says exceeding a posted speed limit. You were charged with driving at a speed which endangers the safety of persons or property. This is nearly impossible to enforce (unless the driver just doesn't want to challenge it) because if you truly were endangering persons or property, you likely would have been charged with something else.
Furthermore, you are protected by California's speed trap laws. This is where I would start. You simply need to call Caltrans and find the person who does the traffic and engineernig surveys for that particular section of highway. The survey must justify the 50mph speed limit. If it doesn't, enforcement of the limit constitutes a speed trap (assuming he used radar or other electronic means to determine your speed). Personally, every person that I have seen who was charged with 22350 and researched the traffic/engineering survey found that the posted limit was unjustified. This is not to suggest that all posted limits are unjustified... but a lot of them are.
I say, do your homework. Tell your parents you got a ticket and then demonstrate to them how you intend to avail yourself of the rights afforded by our govenrment by defending yourself in court. Hopefully, they will be supportive.
Jimbo