SOLUTION: Endpoints of a diameter: (-1, -6) (1, 6)

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Question 627051: Endpoints of a diameter: (-1, -6) (1, 6)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to find the equation of the circle.

Recall that the general equation of a circle is %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2.


So we need the center (h,k) and the radius squared r%5E2.


First, let's find the center (h,k).


Since the center is the midpoint of the line segment with endpoints (-1,-6) and (1,6), we need to find the midpoint.


X-Coordinate of Midpoint = %28x%5B1%5D%2Bx%5B2%5D%29%2F2+=+%28-1%2B1%29%2F2=0%2F2+=+0


Since the x coordinate of midpoint is 0, this means that h=0


Y-Coordinate of Midpoint = %28y%5B1%5D%2By%5B2%5D%29%2F2+=+%28-6%2B6%29%2F2=0%2F2+=+0


Since the y coordinate of midpoint is 0, this means that k=0


So the center is the point (0, 0)


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Now let's find the radius squared


Use the formula r%5E2=%28x-h%29%5E2%2B%28y-k%29%5E2, where (h,k) is the center and (x,y) is an arbitrary point on the circle.


In this case, h=0 and k=0. Also, x=-1 and y=-6. Plug these values into the equation above and simplify to get:


r%5E2=%28-1-0%29%5E2%2B%28-6-0%29%5E2


r%5E2=%28-1%29%5E2%2B%28-6%29%5E2


r%5E2=1%2B36


r%5E2=37


So because h=0, k=0, and r%5E2=37, this means that the equation of the circle that passes through the points (-1,-6) and (1,6) (which are the endpoints of the diameter) is


x%5E2%2By%5E2=37.

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