The points on the curve y2=x3  where normal to the curve makes equal intercepts with the axes is /are

Let foot of normal be (x1,y1) . Theny12=x13 …....(i) Normal makes equal intercepts on axes⇒   −dxdy=±1                 ⇒ dxdy=±1           ⇒ 3x22y|(x1,y1)=±1 ⇒9x144y12=1                     ⇒x1=4/9,         y1=±8/27 Hence; required points are (4/9,±8/27) .