Question

The equation of a circle is (x+1)²+(y-4)²=12 What are the coordinates of the center of the circle?

Answer 1

$\begin{equation*} C(-1,4) \end{equation*}$

1) Since the equation of a circle is defined by:

$(x-a)^2+(y-b)^2=r^2$

And the center is C(a,b)

2) Examining the equation of that circle, we can tell that:

$\begin{gathered} \left(x+1\right)²+\left(y-4\right)²=12\:\Rightarrow C(-1,4) \\ (x-a)^2+(y-b)^2=r^2\Rightarrow C(a,b) \end{gathered}$

2) Thus, the answer is:

$\begin{equation*} C(-1,4) \end{equation*}$