The shortest distance between the line x−y=1 and the curve x2=2y is

Consider the curve x2=2y            Differentiate both sides with respect to x2x=2dydxdydx=xslope of the given line x-y=1 is 1 therefore x=1  Point on the curve   P 1,12     ( since x=1 ⇒ 2y=1 )Eq of tangent to the curve at P is y−12=1(x−1),   y=x−12⇒x−y=12Shortest distance = distance between the parallel lines x-y=1 & x-y=12is   =1−121+1=122