Final answer:
The general equation of the circle is (x - 2)^2 + (y - 3)^2 = sqrt(2)
Step-by-step explanation:
The general equation of a circle with diameter whose endpoints are given can be found using the formula:
(x - h)^2 + (y - k)^2 = r^2
First, find the coordinates of the center of the circle using the midpoint formula:
h = (x1 + x2)/2 and k = (y1 + y2)/2
In this case, the endpoints are (3,4) and (1,2), so the center is (2,3).
Next, find the radius by determining the distance between the center and one of the endpoints:
r = sqrt((x2 - h)^2 + (y2 - k)^2)
Substituting the values, the general equation of the circle is:
(x - 2)^2 + (y - 3)^2 = sqrt(2)