Final answer:
To find the standard equation of a circle with diameter AB, we can find the center point by finding the midpoint between the coordinates of A and B. We can then use the formula (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center point and r is the radius.
Step-by-step explanation:
To find the standard equation of a circle with diameter AB, we can start by finding the center point of the circle. The center point is the midpoint between the coordinates of A and B.
In this case, the coordinates of A are (0, -1) and the coordinates of B are (2, 1). So the midpoint is ((0+2)/2, (-1+1)/2) = (1, 0). Now, we can use the formula (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center point and r is the radius. The radius can be found by calculating the distance between the center point and one of the endpoints, in this case, A or B. The distance formula is sqrt((x2 - x1)^2 + (y2 - y1)^2). So the radius is sqrt((2-1)^2 + (1-0)^2) = sqrt(1 + 1) = sqrt(2). Therefore, the equation of the circle is (x - 1)^2 + (y - 0)^2 = 2.