What is the equation for a line tangent to a circle from a point outside the circle? I need to know the equation for a line tangent to a circle and through a point outside the circle. I have found a number of solutions which involve specific numbers for the circles equation and the point outside but I need a specific solution, i.e., I need an equation which gives me the $m$ and the $b$ in $f(x) = mx + b$ for this line.

The key point is see that the line that is tangent to the circle and intersects your point forms a triangle with a right angle. 
See
https://stackoverflow.com/questions/1351746/find-a-tangent-point-on-circle
