a: \(c o s \alpha = \frac{\mid 3 \cdot 12 + \left(\right. - 4 \left.\right) \cdot \left(\right. - 5 \left.\right) \mid}{\sqrt{3^{2} + \left(\left(\right. - 4 \left.\right)\right)^{2}} \cdot \sqrt{1 2^{2} + \left(\left(\right. - 5 \left.\right)\right)^{2}}} = \frac{\mid 36 + 20 \mid}{5 \cdot 13} = \frac{56}{65}\)

b: (d)//Δ nên (d): 3x-4y+c=0 và c<>7

(C): \(\left(\left(\right. x + 3 \left.\right)\right)^{2} + \left(\left(\right. y - 2 \left.\right)\right)^{2} = 36\)

=>I(-3;2); R=6

(d) tiếp xúc với (C)

=>\(d \left(\right. I ; \left(\right. d \left.\right) \left.\right) = 6\)

=>\(\frac{\mid 3 \cdot \left(\right. - 3 \left.\right) + \left(\right. - 4 \left.\right) \cdot 2 + c \mid}{\sqrt{3^{2} + \left(\left(\right. - 4 \left.\right)\right)^{2}}} = 6\)

=>\(\mid c - 17 \mid = 6 \cdot 5 = 30\)

=>\(\left[\right. c - 17 = 30 \\ c - 17 = - 30 \Leftrightarrow \left[\right. c = 47 \left(\right. n h ậ n \left.\right) \\ c = - 13 \left(\right. n h ậ n \left.\right)\)

Vậy: (d): 3x-4y+47=0 hoặc (d): 3x-4y-13=0