Find the equation of the circle with diameter AB where A is (4, 7) and B is (–2, 3)

Results 1 to 4 of 4

- December 5th 2008, 01:32 AM #1

- Joined
- Nov 2008
- Posts
- 10

- December 5th 2008, 02:29 AM #2

- December 6th 2008, 01:36 AM #3

- Joined
- Nov 2005
- From
- someplace
- Posts
- 14,972
- Thanks
- 4

- December 6th 2008, 02:10 AM #4

- Joined
- Jun 2008
- Posts
- 792

I took the liberty and wrote an explanation. I hope no one has any objections.

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: