Shortest Distance Between Line

Theorem in Plane|| Theorem in Space|| Distance Between Point & a Line|| Distance Between Parallel Lines|| Shortest Distance Between Skew Lines

Consider a hyperbola xy = 4 and a line y = 2x = 4 . O is the centre of hyperbola. Tangent at any point P of hyperbola intersect the coordinate axes at A and B. Shortest distance between the line and hyperbola is

Shortest distance between two parallel lines in vector + cartesian form

Shortest distance between two skew lines in vector + cartesian form

The shortest distance between the lines x+a=2y=-12zandx=y+2a=6z-6a is