Hello, lra11!
Did you make a sketch?
There are a number of approaches to this problem.
Here's one that does not require the points of tangency.
The line contains the origin.
The circle has the equation: .
Its center is and it has radius 2.
It is tangent to the xaxis at Code:

 * * *
 * *
 * *
 B o *
 * 2
 * * *
 * * oC *
 * * : *
 * :
 * θ * * :2 *
 * * : *
 * θ * : *
 o .          * o *      
O 3 A
Obviously, one tangent is: .
Let
The slope of is: .
From congruent right triangles,
The slope of is: .