SAT Mathematics Practice Test 2

The equation of a circle with center $\left(\mathit{h},\mathit{k}\right)$ and radius $\mathit{r}$ is ${\left(\mathit{x}-\mathit{h}\right)}^2+{\left(\mathit{y}-\mathit{k}\right)}^2={\mathit{r}}^2$.To put the equation ${\mathit{x}}^2+{\mathit{y}}^2+4\mathit{x}-2\mathit{y}=-1$ The equation of a circle with center (h, k) and radius $\mathit{r}$${\mathit{x}}^2+{\mathit{y}}^2+4\mathit{x}-2\mathit{y}=-1$
$\left({\mathit{x}}^2+4\mathit{x}\right)+\left({\mathit{y}}^2-2\mathit{y}\right)=-1$
$\left({\mathit{x}}^2+4\mathit{x}+4\right)-4+\left({\mathit{y}}^2-2\mathit{y}+1\right)-1=-1$
${\left(\mathit{x}+2\right)}^2+{\left(\mathit{y}-1\right)}^2-4-1=-1$
${\left(\mathit{x}+2\right)}^2+{\left(\mathit{y}-1\right)}^2=4=2^2$
Therefore, the radius of the circle is 2.
Choice C is incorrect because it is the square of the radius, not the radius. Choices B and D are incorrect and may result from errors in rewriting the given equation in standard form.