Let B denote a curve y=yx which is in the first quadrant and let the point 1,0  lie on it. Let the tangent to B at a point P intersect the y−axis  at YP If PYP  has length 1 for each point P on B, then which of the following options is/are correct?

Equation of tangent at Px,y  is  Y-y= dydxX-x  ⇒  xdy−ydx=xdy−ydx .So Yp=y−xdydx  since X=0 Distance between Px,y and YP0,y-xdydx=PYP=x2+x2dydx2=1  ⇒dydx=±1-x2x  So ∫dy=±∫1-x2xdx =±∫1-x2x1-x2dx =±∫xdxx21-x2-∫xdx1-x2   Let 1-x2=t2⇒xdx=-tdt  So y=±-∫tdt1-t2t+∫tdtt   =±12lnt-1t+1+t y=-ln1+1-x2x+1-x2+c y=ln1+1-x2x-1-x2+C        put x=1 and y=0   then  c=0 but as function lies in 1st quadrant so y=ln1+1−x2x−1−x2 & dydx=−1−x2x