SAT Mathematics Practice Test 5

The standard equation of a circle in the $\mathit{x}\mathit{y}-$plane is of the form ${\left(\mathit{x}-\mathit{h}\right)}^2+{\left(\mathit{y}-\mathit{k}\right)}^2={\mathit{r}}^2,$ where$\left(\mathit{h},\mathit{k}\right)$ are the coordinates of the center of the circle and r is the radius. To convert the given equation to the standard form, complete the squares. The first two terms need a 100 to complete the square, and the second two terms need a 64. Adding 100 and 64 to both sides of the given equation yields ,which is equivalent to ${\left(\mathit{x}+10\right)}^2{\left(\mathit{y}+8\right)}^2=144$.Therefore, the coordinates of the center of the circle are $\left(-10,-8\right)$.Choice A is incorrect and is likely the result of not properly dividing when attempting to complete the square. Choice C is incorrect and is likely the result of making a sign error when evaluating the coordinates of the center. Choice D is incorrect and is likely the result of not properly dividing when attempting to complete the square and making a sign error when evaluating the coordinates of the center.