1. branch a C( 1, 0) and point a is on ⊙C, k_AC=(2-0)/(2- 1)=2? Therefore, the slope k of the tangent line =-1/2.

The tangent equation is y-2=-(x-2)/2? X+2y-6=0。

2. At this time, point A is outside ⊙C, and the tangents are B and D. It is easy to know that AC=2√2? CB=CD=√5

So tan∠CAD=CD/AC=√ 10 is given by the included angle formula | k-1|1+k | = √10.

Get k =-(112 √10)/9? So the tangent equation is y-2 =-(112 √10) (x-3)/9.