Answer:
[tex](x+9)^2+(y-4)^2=81[/tex]
Step-by-step explanation:
If the circle has the center at point (a,b) and radius r units, then its equation in standard form is
[tex](x-a)^2+(y-b)^2=r^2[/tex]
In your case, the center of the circle is at point (-9,4). This circle is tangent to the y-axis, then it is tangent to the y-axis at point (0,4). The radius of the circle is the distance between the center and the tangent point:
[tex]r=\sqrt{(-9-0)^2+(4-4)^2}=\sqrt{81+0}=9[/tex]
Thus, the equation of the circle is
[tex](x-(-9))^2+(y-4)^2=9^2\\ \\(x+9)^2+(y-4)^2=81[/tex]
