Question

Write an equation that represents each circle.

Answer 1

`\boxed{1}\\\\ \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{h}{-2}~~,~~\underset{k}{4})} \qquad \stackrel{radius}{\underset{r}{4}} \\\\[-0.35em] ~\dotfill\\\\( ~~ x - (-2) ~~ )^2 ~~ + ~~ ( ~~ y-4 ~~ )^2~~ = ~~4^2\implies (x +2)^2 + (y -4)^2 = 16 \\\\[-0.35em] ~\dotfill\\`

`\boxed{2}\\\\ \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{h}{0}~~,~~\underset{k}{0})} \qquad \stackrel{radius}{\underset{r}{8}} \\\\[-0.35em] ~\dotfill\\\\( ~~ x - 0 ~~ )^2 ~~ + ~~ ( ~~ y-0 ~~ )^2~~ = ~~8^2\implies x^2 + y^2 = 64`