Question

Find the center and the radius of the circle with the equation x^2+y^2=42

Answer 1

$\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r}\\\\ -------------------------------\\\\ x^2+y^2=42\implies (x-\stackrel{h}{0})^2+(y-\stackrel{k}{0})=(\stackrel{r}{\sqrt{42}})^2~~ \begin{cases} center~(0,0)\\ radius=\sqrt{42} \end{cases}$