Question

what is the standard form of the equation of a circle with its center at (2,-3) and passing through the point (-2,0) ?

Answer 1

you know it looks like
\[(x-h)^2+(y-k)^2=r^2\] and you know \((h,k)\) is \((2,-3)\) the only number you don't know is \(r^2\)

Answer 2

find that via the distance formula (pythagoras)
\[r^2=(2+2)^2+3^2\]