Let y=y(x) be a function of x satisfying  y1−x2=k−x1−y2where k is a constant y12=−14and . Then  dydxat x=12 is equal to:

At x=12,y=−14⇒xy=−18.Differentiating w.r.t. x, we gety.1.-2x21−x2+y'.1−x2=−1.1−y2+x.−2y21−y2y'⇒−xy1−x2+y'1−x2=−1−y2+xy.y'1−y2⇒y'1−x2−xy1−y2=xy1−x2−1−y2⇒y'32+18.154=−1832−154⇒y'45+1215=-1+4543⇒y'=dydxx=12=-52