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
      $(x-k{)}^2+(y-2{)}^2=k^2$

which passes through the point $(–1, 0)$
if $(-1-k{)}^2+4=k^2\Rightarrow k=-5/2$

and the equation of the circle is

  $x^2+y^2+5x-4y+4=0$
which passes through $(–4, 0)$