Question

Find an equation of the circle that has a center (6,0) and passes through (-3,-6)

Answer 1

To find the equation, we use the standard form

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

So, we replace the center and the given point to find the radius r

$(-3-6)^2+(-6-0)^2=r^2$

Now, we solve for r

$\begin{gathered} r^2=(-9)^2+(-6)^2 \\ r^2=81+36 \\ r^2=117 \end{gathered}$

Hence, the equation of the circle is

$(x-6)^2+y^2=117$