Respuesta :
the equation is in standard form
[tex] {x}^{2} + {(y + 8)}^{2} = 64[/tex]
[tex] {x}^{2} + {(y + 8)}^{2} = 64[/tex]
An equation of a circle having radius equal to [tex]8[/tex] and center equal to [tex](0,-8)[/tex] is [tex]\boldsymbol{x^2+y^2+16y=0}[/tex]
Equation of a circle
A circle is a shape made up of all points in a plane that are at the same distance from a central point.
Standard form for the equation of a circle is [tex]\boldsymbol{(x-h)^2+(y-k)^2=r^2}[/tex] where [tex]\boldsymbol{(h,k),r}[/tex] denote center and radius of a circle respectively.
Center is [tex]\boldsymbol{(0,-8)}[/tex] and radius is equal to [tex]\boldsymbol{8}[/tex] units.
So, an equation is [tex](x-0)^2+(y+8)^2=8^2[/tex]
[tex]x^2+y^2+64+16y=64[/tex]
[tex]x^2+y^2+16y=0[/tex]
So, an equation of a circle having radius equal to [tex]8[/tex] and center equal to [tex](0,-8)[/tex] is [tex]\boldsymbol{x^2+y^2+16y=0}[/tex]
Find out more information about circle here:
https://brainly.com/question/11833983?referrer=searchResults
