Find the equation of the circle with diameter AB where A is (4, 7) and B is (–2, 3)
Before starting, I want to point out a mistake in 4. We have found the radius to be . Therefore, is 13 and not 13/2.
To find the equation of the circle with the given information, we need two things: the magnitude of the radius and the coordinate of the center. Recall that the equation of the circle is of the form:
where (h, k) are the coordinates of the center and r is the radius.
1. Taking the average of the individual x and y coordinates yields the midpoint of diameter AB, which is also the center of the circle.
2. Using the distance formula:
we find the measure of the diameter AB. Dividing it by 2 yields the radius.
3 & 4. Replacing in the equation of the circle yields: