# Identify the curve by finding a Cartesian equation for the

Identify the curve by finding a Cartesian equation for the curve. $$\displaystyle{r}^{{2}}={5}$$

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Ourst1977
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 $$\displaystyle\sqrt{{{5}}}$$