The general point on Hyperbola is (2rt6seck,3rt2tank).Calculate the dis. of this point from the line using the formula and it proves to be min iff rt3seck+tank is min.

The critical points occur at sink=-1/rt3 and there are two points one in 2nd and other in 4th quadrant[plot a rough graph] where the distance might be min.If we substitute corresponding values of seck and tank taking the corresponding signs,the dis comes out to be min for the point in Q₄  and the point is (6,-3)