The curve such that at an point of it the square of the ordinate is twice the product of the x-intercept of the normal and the obscissa, is

Normal at P(x,y) is (Y−y)y1+X−x=0 Its x -intercept =x+y⋅y12xx+y⋅y1=y2xx+y⋅y1=y2⇒2yy1-y2x =-2x⇒dy2dx−y2x=−2xI.F=1x Soln is y2x=∫−2x⋅1xdx=−2x+c⇒y2+2x2=cx