Given that

\(\displaystyle{r}^{{2}}={5}\)

Recall that: \(\displaystyle{r}^{{2}}={x}^{{2}}+{y}^{{2}}\)

Therefore we have

\(\displaystyle{x}^{{2}}+{y}^{{2}}={5}\)

This can be rewrittena as

\(\displaystyle{\left({x}-{0}\right)}^{{2}}+{\left({y}-{0}\right)}^{{2}}={\left(\sqrt{{{5}}}\right)}^{{2}}\)

This is equation of a circle with centre at (0,0) and radius \(\displaystyle\sqrt{{{5}}}\)

Result:

That is equation of a circle with at (0,0) and radius \(\displaystyle\sqrt{{{5}}}\)

\(\displaystyle{r}^{{2}}={5}\)

Recall that: \(\displaystyle{r}^{{2}}={x}^{{2}}+{y}^{{2}}\)

Therefore we have

\(\displaystyle{x}^{{2}}+{y}^{{2}}={5}\)

This can be rewrittena as

\(\displaystyle{\left({x}-{0}\right)}^{{2}}+{\left({y}-{0}\right)}^{{2}}={\left(\sqrt{{{5}}}\right)}^{{2}}\)

This is equation of a circle with centre at (0,0) and radius \(\displaystyle\sqrt{{{5}}}\)

Result:

That is equation of a circle with at (0,0) and radius \(\displaystyle\sqrt{{{5}}}\)