A yellow light ticket

I was driving south to down town Washington DC with a passenger in the car, the light turned yellow before I got to the white line. I had time to make the light so I went through it. There was a cop parked after the intersection on the opposite side of the road and he pulled me over to give me a ticket for going through the yellow light. Note I: The only way he could have known I went through the yellow light is that the light that is parallel to the light I went through changes at the same time. Note II: I tried to dispute the ticket with the officer; he said he could give me a red light ticket for the reason that when I passed under the light, it turned red. II a: The passenger and I did not see that the light turned red. II b: He said he is doing me a favor by giving me a yellow light ticket instead of a red light ticket. Note III: The passenger in the car can verify that the light turned yellow and that we did not accelerate to go through the light. Background Info: My driving record is not the best, 5 points that I know of. The ticket is $75.00 and 2 points. Can someone please recommend what I should do? I want to have the ticket thrown out because there are no real bases for a yellow light ticket. Thank you