Question

I will be attaching a picture of the question as you can see the question has already been answered my teacher wants me to type out how she got the answer I need it fast bc this is due in an hour.

Answer 1

we calculate the radius, i.e. the distance between two points

$\begin{gathered} r=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ r=\sqrt[]{(-1-2)^2+(-8-(-3))^2} \\ r=\sqrt[]{(-3)^2+(-8+3)^2} \\ r=\sqrt[]{(-3)^2+(-5)^2} \\ r=\sqrt[]{9+25} \\ r=\sqrt[]{34} \end{gathered}$

then, we have that the equation of the circle is

$\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where} \\ h=2 \\ k=-3 \\ r^2=(\sqrt[]{34})^2=34 \end{gathered}$

therefore the equation is

$\begin{gathered} (x-2)^2+(y-(-3))^2=34 \\ (x-2)^2+(y+3)^2=34 \end{gathered}$