Let (h,k) be center of circle.Circle touches the y-axis.
∴ Radius of circle =h
Equation of circle-
(x−h)2+(y−k)2=h2.....(1)Since the circle passes through (0,2)
Therefore,
h2+(2−k)2=h2
⇒(k−2)2=0
⇒k=2
Given that the circle also passes through (−1,0),
Therefore,
(−1−h)2+22=h2
h2+1+2h+4=h2
h=−25
Substituting the value of h and k in eqn(1), we get
(x+25)2+(y−2)2=(25)2
Now, we can find the point from which the circle passes.
As the point (4,0) satisfy the equation of circle.
Thus, the circle will also pass through the point (−4,0).
Hence the correct answer is (D)(−4,0).