Equation of family of circles whose radius is 4 is : (x−a)2+(y−b)2=16......(i) (where a & b are arbitrary constant) Differentiating we get: 2(x−a)+1(y−b)y1 .......(ii) (y1=
dy
dx
) Again differentiating we get: 1+y1.y1+(y−b)y2=0(y2=
d2y
dx2
) ⇒(y−b)y2+(y−b)y2=0 (y−b)y2=−(1+y12) ⇒y−b=
(1+y12)
y2
......(iii) from (ii) we get : x−a=−(y−b)y1 ∴ from (i) , we get : (y−b)2y12+(y−b)2=16 ⇒(y−b)2−(1+y12)=16 ⇒(