Answer:
[tex]\large\boxed{(x-4)^2+(y+3)^2=25}[/tex]
Step-by-step explanation:
The equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the center (4, -3) and the point on the circle (9, -3).
The length of radius is equal to the distance between a center and an any point on a circle.
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Susbtitute:
[tex]r=\sqrt{(9-4)^2+(-3-(-3))^2}=\sqrt{5^2+0^2}=\sqrt{5^2}=5[/tex]
The center (4, -3) → h = 4, k = -3.
Finally we have:
[tex](x-4)^2+(y-(-3))^2=5^2\\\\(x-4)^2+(y+3)^2=25[/tex]
