Hello, atruenut!
There are two tangent lines from the point (0,1) to the circle
Find equations of these tangents. Code:

P * (0,1)
/\
. /  \
/  \
/  \
/  \
    /  * * *  \      
/*  *\
o  o A
* *  * *
*  *
* *  * *
* C *(0,1) *
*  *

*  *
*  *
*  *
* * *

The center of the circle is:
Its radius is:
A radius is perpendicular to a tangent at the point of tangency.
. . Hence: .
In right triangle we have: .
. . Hence, is a 3060 right triangle . . .
You should be able to determine the slope of . . . right?