The circle passing through the point (–1, 0) and touching y-axis at (0, 2) also passes through the point

Let he equation of the circle be      (x−k)2+(y−2)2=k2which passes through the point (–1, 0)if (−1−k)2+4=k2⇒k=−5/2and the equation of the circle is  x2+y2+5x−4y+4=0which passes through (–4, 0)