I think this is wrong because point P is (-2, 15), not (-2, 2). Thank you for your answer though.

I don't think UV=r because U is outside the circle.

Could you tell me why we need ax^{2} + (b+11)x + 8 = 0 to have equal roots at x = 2?

Thank you so much for your thorough answer. Could you tell me how to solve this problem without using calculus?

Thank you for your answers.

Could you explain how you got those answers, please?

I still don't understand how you got 32 for angle ACB. Could you explain it in more detail?

Are there any other ways?

Thanks for your answer. Could you explain how you got your answers, please?