The general equation of a circle is expressed as
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2\text{ ----- equation 1} \\ \text{where} \\ (a,\text{ b)}\Rightarrow\text{ center of the circle} \\ r\Rightarrow radius\text{ of the circle} \end{gathered}[/tex]
Given that a circle having equation
[tex]\begin{gathered} (x-2)^2+(y-5)^2\text{ = 16} \\ \Rightarrow(x-2)^2+(y-5)^2\text{ = }4^2 \end{gathered}[/tex]
is moved up 3 units and 1 unit to the left. Thus, we have
[tex]\begin{gathered} (x-2+1)^2+(y-5-3)^2\text{ = }4^2 \\ \end{gathered}[/tex]
This gives
[tex](x-1)^2+(y-8)^2\text{ = }4^2\text{ ----- equation 2}[/tex]
Comparing equations 1 and 2, we have
[tex]a\text{ = 1, b = 8, r = 4}[/tex]
Hence,
the center (a, b) of the circle is (1, 8),
the radius r of the circle is 4,
the equation of the circle is
[tex](x-1)^2+(y-8)^2=4^2[/tex]
