Answer:
Option B,C
Explanation:
Since the centre lies on y=x.
∴ Equation of circle is
x^{2}+y^{2}-2ax-2ay+c=0
On differentiating , we get
2x+2yy'-2a-2ay'=0
\Rightarrow x+yy'-a-ay'=0
\Rightarrow a=\frac{x+yy'}{1+y'}
Again differentiating , we get
0 = \frac{(1+y')[1+yy'+(y')^{2}]-(x+yy').(y")}{(1+y')^{2}}
\Rightarrow (1+y')[1+(y')^{2}+yy"]- (x+yy')(y")=0
\Rightarrow 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