the circle touches the x axis at the orgin so the center must lie on the y axis..

 

let center be (0,a)..

 

now radius is also equal to 'a' in this case..

 

ther4 eqn of circle is ..

 

x² + (y-a)² = a²

 

=> a = (x² + y²) / 2y

 

differentiating the eqn of circle once only since we have only one parameter "a".

 

we have

 

dy/dx = x/a-y

 

substitute value of a ..

 

answer is .