Respuesta :
Answer:
(5,-6)
Step-by-step explanation:
When you write the equation of a circle in the form
[tex](x-x_0)^2+(y-y_0)^2=r^2[/tex]
Then the center of the circle will be [tex](x_0,y_0)[/tex] and the radius will be [tex]r[/tex].
Answer: The center of the given circle is (5, -6).
Step-by-step explanation: We are given to find the center of the circle represented by the following equation :
[tex](x-5)^2+(y+6)^2-4^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the STANDARD equation of a circle with center (h, k) and radius r units is given by
[tex](x-h)^2+(y-k)^2=r^2.[/tex]
From equation (i), we have
[tex](x-5)^2+(y+6)^2=4^2\\\\\Rightarrow (x-5)^2+(y-(-6))^2=4^2.[/tex]
Comparing with the standard form, we get that the center of the given circle is (h, k) = (5, -6).
Thus, the center of the given circle is (5, -6).
