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Sagot :
Step 1
Define the equation of a circle
[tex]\text{The equation of a circle = (x-h)}^2+(y-k)^2=r^2[/tex]Step 2
Write down the parameters
r = radius = ?
h = -6
k = 4
Step 3
find the radius
Considering the triangle we can find the radius using the Pythagoras theorem
[tex]r^2=5^2+12^2[/tex][tex]\begin{gathered} r\text{ = }\sqrt[\square]{25\text{ + 144}} \\ r\text{ = }\sqrt[]{169} \\ r\text{ = 13} \end{gathered}[/tex]Step 3
Substitute the values into the equation and simplify
[tex]\begin{gathered} (x-(-6))^2+(y-4)^2=13^2 \\ (x+6)^2+(y-4)^2=13^2 \end{gathered}[/tex]Answer is option A
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