KEAM 2013 Math Paper

The equation of family of circles of fixed radius' r′ with centres on the y -axis is
(x−0)2+(y−a)2=r2.....(i)
On differentiating w.r.t. x, we get
2x+2(y−a)‌

dy

dx

=0
⇒‌‌‌

dy

dx

=−‌

x

y−a

⇒‌‌(y−a)=‌

−x

(dy/dx)

On putting this value in Eq. (i), we get
x2+‌

x2

(‌ dy dx )2

=r2
⇒‌‌x2{1+(‌

dy

dx

)2}=r2(‌

dy

dx

)2
Hence, order → highest order derivative =1 and degree → power of highest order derivative =2