Question

which of the following graphs matches the circle defined by this equation? (x - 2)^2+(y + 3)^2 = 16

Explanation:

Step1: Identify the center and radius formula

The standard - form of a circle equation is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center of the circle and $r$ is the radius.

Step2: Determine the center of the circle

For the equation $(x - 2)^2+(y+3)^2 = 16$, comparing with the standard form, we have $h = 2$ and $k=-3$. So the center of the circle is $(2,-3)$.

Step3: Determine the radius of the circle

Since $r^2 = 16$, then $r=\sqrt{16}=4$.

Step4: Analyze the graphs

Graph C has a center at $(2,-3)$ and a radius of 4.

Answer:

C.