Answer:
[tex]\large\boxed{(x-5)^2+(y+7)^2=36}[/tex]
Step-by-step explanation:
The equation of a circle in standard form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We hace the center at (5, -7) → h = 5 and k = -7.
The radius is equal to the distance petween the center and other point on the circumference of a circle.
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute the coordinates of the points (5, -7) and (5, -1):
[tex]d=\sqrt{(5-5)^2+(-1-(-7))^2}=\sqrt{0^2+6^2}=\sqrt{36}=6[/tex]
Therefore the equation of a circle is:
[tex](x-5)^2+(y-(-7))^2=6^2\\\\(x-5)^2+(y+7)^2=36[/tex]
