Question

what is the center and radius of the circle?(x - 6)² + (y + 8)² = 81

Answer 1

The general equation for a circle is:

$(x-h)^2+(y-k)^2=r^2$

where (h,k) is the center and r is the radius.

In this case, we have the following:

$(x-6)^2+(y+8)^2=81$

Notice that we can write the equation in the following way:

$\begin{gathered} (x-6)^2+(y+8)^2=81 \\ \Rightarrow(x+6)^2+(y-(-8))^2=(9)^2 \end{gathered}$

therefore, the center of the circle is (h,k)=(6,-8) and the radius is r=9