Explanation:
The equation of a circle with center located at (x1, y1) and radius r is:
[tex](x-x_1)^2+(y-y_1)^2=r^2[/tex]
We have the point but we need to find r. For that we can use the equation of the circumference:
[tex]C=2\pi r[/tex]
We have C = 16pi:
[tex]\begin{gathered} 16\pi=2\pi r \\ \frac{16\pi}{2\pi}=r \\ r=8 \end{gathered}[/tex]
Now we have r = 8, therefore r²=64. The answers could be either option 1 or option 3. To find out which one is it we have to check the point.
If the point is (-2, -2) then the part with x is (x - (-2))² = (x+2)² and the part with y is (y - 2)²
Answer:
The correct equation is option 3:
[tex](x+2)^2+(y-2)^2=64[/tex]
