$\displaystyle 2x^{2}+y^{2}-3xy=0$ be the equation of pair of tangents drawn from the origin O to circles of radius $3$. Find the absolute difference of all possible different lengths of tangents.

The equation 2x^2 + y^2 - 3xy = 0 factors into (2x - y)(x - y) = 0. The tangents are y = 2x and y = x. The distance from the center of a circle (h, k) to a line ax + by + c = 0 is r. Since the tangents are from the origin, the center of the circle must be at a distance of 3 from both lines. This leads to a specific geometric configuration. The absolute difference of the lengths of the tangents is 18.