SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given details
[tex]\begin{gathered} center\text{ }(7,-1) \\ radius=2 \end{gathered}[/tex]STEP 2: Write the formula for the equation of a circle
[tex]\begin{gathered} \left(x−a\right)^2+\left(y−b\right)^2=r^2\:\:\mathrm{is\:the\:circle\:equation\:with\:a\:radius\:r,\:centered\:at}\:\left(a,\:b\right) \\ \mathrm{Plug\:in}\:\left(7,\:-1\right),\:r=2 \\ \left(x-7\right)^2+\left(y-\left(-1\right)\right)^2=2^2 \\ \left(x-7\right)^2+\left(y+1\right)^2=4 \end{gathered}[/tex]Hence, the equation of the circle is given as:
[tex]\left(x-7\right)^2+\left(y+1\right)^2=4[/tex]