U wud want to give me 2 salutes for this method......

 

 

The condition for shortest or longest distance from a point is the length of the normal to the curve that passes thru the point..

 

Find dy/dx for the given curve......

 

For the slope of the normal to be y/x, the slope of the tangent must b -x/y

 

Equate the two u get a simple relation b/w the absicca and the ordinate of the points having extremum distances from the origin...(the relation is x^2 = y^2)

 

Put them in the eqn of the curve and get the points.

Find the dist, their sum or watever u wish to find out.......