Thanks and have a nice day.Given: A circle with centre T(5, -1) and radius of 16
To Determine: The equation of the circle
The equation of a circle with the coordinate of the centre and radius is
[tex]\begin{gathered} \text{center}=(h,k) \\ \text{radius}=r \\ \text{The equation of the circle is} \\ (x-h)^2+(y-k)^2=r^2 \end{gathered}[/tex]
From the given center and radius, we have
[tex]\begin{gathered} CenterT=(5,-1) \\ h=5,k=-1 \\ \text{radius}=r=16 \end{gathered}[/tex]
Substitute the values of h, k, and r into the equation of the circle as shown below:
[tex]\begin{gathered} (x-5)^2+(y--1)^2=16^2 \\ (x-5)^2+(y+1)^2=256 \end{gathered}[/tex]
Hence, the equation of the circle with center T(5,-1) and radius 16 is
(x-5)²+(y+1)²=256, OPTION B
