Respuesta :

the standard equation of a circle is (x-h)²+(y-k)²=r², (h,k) is the center, r is the radius.
You have the center (0,-8), you need the radius.
the radius is the distance between the center and any point on the circle.
use the distance formula, r=√(2-0)²+(-5-(-8))²=√13
so the equation is x²+(y+8)²=13

The equation of the circle is [tex]x^2+(y+8)^2=13[/tex]

Calculation of the equation of the circle:

Since we know that

The standard equation of a circle should be

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where,(h,k) is the center, r is the radius.

Since the center (0,-8), so here the radius need to be determined

the radius refers to the distance between the center and any point on the circle.

So here we used the distance formula

[tex]r=\sqrt (2-0)^2+(-5-(-8))^2=\sqrt 13[/tex]

so the equation is [tex]x^2+(y+8)^2=13[/tex]

Learn more about the circle here: https://brainly.com/question/3401487