Consider the family of all circles whose centres lie on the straight liney=x if this family of circles is represented by the differential equation Py11+Qy1+1=0where P,Q are functions of  x,yand y1(here y1=dydx,y11=d2ydx2), then which of the following statements is (are) true?

The general equation of family of circles whose center lies on line y=x isx2+y2-2ax-2ay+c=0Differentiating w.r.t. x, we get2x+2yy1-2a-2ay1=0⇒a=x+yy11+y1 Diff. w.r.t x1+y11+yy11+y12-x+yy1y11=0⇒(y-x)y11+y11+y1+y12+1=0 Comparing with G. E. P=y-x; Q=1+y1+y12P+Q=1-x+y+y1+y12∴options (2),(3) are correct