Answer:
Option B,C
Explanation:
Since the centre lies on y=x.
∴ Equation of circle is
x2+y2−2ax−2ay+c=0
On differentiating , we get
2x+2yy′−2a−2ay′=0
⇒ x+yy′−a−ay′=0
⇒ a=x+yy′1+y′
Again differentiating , we get
0 =(1+y′)[1+yy′+(y′)2]−(x+yy′).(y")(1+y′)2
⇒ (1+y′)[1+(y′)2+yy"]−(x+yy′)(y")=0
⇒ 1+y′[(y′)2+y′+1]+y"(y−x)=0
On comparing with Py"+Qy′+1=0, we get
P=y-x and Q=(y′)2+y′+1