Answer:
[tex](x - 5)^2 + (y + 6)^2 = 10[/tex]
Step-by-step explanation:
The equation of a circle is given by:
[tex] \Large\boxed{\boxed{(x - h)^2 + (y - k)^2 = r^2}} [/tex]
where [tex](h, k)[/tex] is the center of the circle, and [tex]r[/tex] is the radius.
In this case, the center of the circle is given as [tex](5, -6)[/tex] and a point on the circumference is given as [tex](6, -3)[/tex].
First, we can find the radius ([tex]r[/tex]) using the distance formula between the center and a point on the circumference:
[tex] r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
[tex] r = \sqrt{(6 - 5)^2 + (-3 - (-6))^2} [/tex]
[tex] r = \sqrt{1^2 + 3^2} [/tex]
[tex] r = \sqrt{1 + 9} [/tex]
[tex] r = \sqrt{10} [/tex]
Now that we have the radius, we can substitute the values into the equation of the circle:
[tex] (x - 5)^2 + (y + 6)^2 = 10 [/tex]
So, the equation of the circle is:
[tex](x - 5)^2 + (y + 6)^2 = 10[/tex]
