I encountered this problem months ago in a math competition, and have yet to have any understanding how it could be solved.

A non-vertical line with y-intercept 2 is tangent to the curve given by the equation x^2 + y^2 = 12x + 20y - 100. Find the slope of the line.

This problem would be easy if it was single variable, but because it has both x and y, I have zero clue where to start.