Question

how can you use the definition of a circle and the distance formula to derive the standard equation of a circle?

Answer 1

circle definition : a round plane figure whose boundary (the circumference) consists of points equidistant (=radius r) from a fixed point (the center (h,k)).

let (x,y) is a point on the circle.
its distance (r) to center is
(x-h)^2 + (y-k)^2 = r^2
... the circle equation