BITSAT 2006 Solved Question Paper

Since, the circle touches the y-axis, therefore the centre lies on the x-axis. Let the centre be (h,0).
⇒ Radius of circle =h. ∴ The equation of circle is given by
(x−h)2+(y−0)2=h2
⇒x2+y2−2hx=0 ...(i)
On differentiating both sides w.r.t. x, we get
2x+2y

dy

dx

−2h=0
⇒h=x+y

dy

dx

Putting the value of h in Eq. (i)
x2+y2−2x(x+y

dy

dx

)=0
⇒−x2+y2−2xy

dy

dx

=0
⇒x2−y2+2xy

dy

dx

=0
This is the required differential equation.