Explanation:
remember, the general equation for a circle is
(x - h)² + (y - k)² = r²
r is the radius, (h, k) is the center point of the circle.
the line (0, 8) to (0, -2) is a diameter, so, the center of the circle is the midpoint between both points.
remember, the midpoint between 2 points (x1, y1) and (x2, y2) is
((x1+x2)/2, (y1+y2)/2)
in our case :
((0+0)/2, (8-2)/2) = (0, 3)
the distance from the center point to the endpoint is e.g
(0, 3) to (0,8) = 8-3 = 5.
and that is the radius.
the equation of the circle is therefore :
(x - 0)² + (y - 3)² = 5²
x² + (y - 3)² = 25