Question

18. What is the center and radius of the circle with equation (x - 5)² + (y + 3)² = 16?center (-5, 3); radius = 16center (3,-5); radius = 4center (5,-3); radius = 4center (5,-3); radius = 16

Answer 1

The given data for this problem is the equation of a circle. We need to find the coordinates of the center and radius.

The equation of a circle has the following form:

$(x-x_c)^2+(y-y_c)^2=R^2$

When we compare the equation given to us, we have:

$\begin{gathered} -x_c=-5\rightarrow x_c=5\\ \\ -y_c=3\rightarrow y_c=-3\\ \\ R^2=16\rightarrow R=4 \end{gathered}$

The center is at (5, -3) and the radius is 4. The correct answer is the third option.