Respuesta :
Given a circle that has its center at:
[tex](-16,30)[/tex]You know that it passes through the Origin:
[tex](0,0)[/tex]By definition, the equation of a circle has this form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where "r" is the radius of the circle and the center of the circle is:
[tex](h,k)[/tex]In this case, knowing that the radius of a circle is the distance from its center to a point on the circle, you need to find the distance between the center and the Origin. To do this, you can use the formula for calculating the distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}^[/tex]Where these are the two points:
[tex]\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}[/tex]In this case, you can set up that:
[tex]\begin{gathered} x_2=-16 \\ x_1=0 \\ y_2=30 \\ y_1=0 \end{gathered}[/tex]Then, you get:
[tex]d=r=\sqrt{(-16-0)^2+(30-0)^2}^=\sqrt{1156}=34[/tex]Now you can determine that:
[tex]r^2=34^2=1156[/tex]You can also identify that:
[tex]\begin{gathered} h=-16 \\ k=30 \end{gathered}[/tex]Therefore, you can determine that the equation of the given circle is:
[tex](x-(-16))^2+(y-30)^2=1156[/tex][tex](x+16)^2+(y-30)^2=1156[/tex]Hence, the answer is: Option B.
