The point on the line 3x−2y=1  which is closest to the origin is

The point can be taken as (x,3x−12) Let z=x2+(3x−1)24[where z= Square of the distance of the point from origin]z  is min. for x=313∴  The point is (313,−213)second method:   Nearest point from 0,0 to 3x-2y-1=0 is equal to foot of the perpendicular  drawn from 0,0  to the line . Let h,k be the foot of origin on the given line. therefore h-03=k-0-2=--132+22 ⇒h=313 and k=-213