Hello, atruenut!
There are two tangent lines from the point (0,1) to the circle $\displaystyle x^2 + (y+1)^2\:=\:1$
Find equations of these tangents. Code:

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

*  *
*  *
*  *
* * *

The center of the circle is: $\displaystyle C(0,1)$
Its radius is: $\displaystyle CA = 1$
A radius is perpendicular to a tangent at the point of tangency.
. . Hence: .$\displaystyle \angle CAP \:=\:90^o$
In right triangle $\displaystyle CAP$ we have: .$\displaystyle CA = 1,\;CP = 2$
. . Hence, $\displaystyle \Delta CAP$ is a 3060 right triangle . . . $\displaystyle \angle APC = 30^o$
You should be able to determine the slope of $\displaystyle PA$ . . . right?