Respuesta :
In order to determine the equation of the given circle, take into account the general formula for the equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where the point (h,k) is the center of the circle.
You have tha the center of the circle is (-16,30). It means that:
h = -16
k = 30
then, the left side of the equation becomes:
[tex]\begin{gathered} (x-(-16))^2+(y-30)^2 \\ =(x+16)^2+(y-30)^2 \end{gathered}[/tex]next, consider that if the point passestroug the origin, it is necessary that for
x = 0 and y = 0 the equation coincides with one of the given options.
Replace x=0 and y=0 in the following expression:
[tex](0+16)^2+(0-30)^2=1156[/tex]Hence, it is necessary taht r^2 = 1156
The requierd equation of the circle is:
[tex](x+16)^2+(y-30)^2=1156[/tex]
