Question

The equation of a circle is given below.(X+ 4)2 + (y – 6)2 = 48What is its center? ?What is its radius?If necessary, round your answer to two decimal places.units

Answer 1

$\begin{gathered} \text{Equation of a circle center (h,k) with radius r is given as } \\ (x-h)^2+(y-k)^2=r^2 \end{gathered}$

comparing the given equation with the equation of a circle, we have:

$\begin{gathered} x+4=\text{ x-h} \\ x-x+4=-h \\ -h=4 \\ h=-4 \\ \\ \text{Also,} \\ y-6=y-k \\ y-y-6=-k \\ -k=-6 \\ k=6 \\ \\ r^2=48 \\ r=\sqrt[]{48} \\ r=6.928 \\ r=6.93(2\text{ decimal places)} \end{gathered}$

The center is (-4, 6) and the radius is 6.93