Question 143180: write the equation of the information given.
endpoints of a diameter are (6,9) and (20,7)
Found 2 solutions by scott8148, rapaljer:
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! the center is the midpoint of the diameter __ [(6+20)/2,(9+7)/2] __ (13,8)
the radius is the distance from the mid-point to one end __ r^2=(20-13)^2+(7-8)^2 __ r^2=49+1 __ r^2=50
(x-13)^2+(y-8)^2=50
Answer by rapaljer(4671)  (Show Source):
You can put this solution on YOUR website! Assuming that the problem is to find the equation of a circle with end points of diameter at these two points, the first step is to find the center of the circle, which is the midpoint of these two points. To find the midpoint of two points, it's like the average of the x coordinates (add together and divide by 2), and the average of the y coordinate.
(6,9) and (20,7)
Next, find the radius, which is the distance from the center to either endpoint. For example, between (6,9) and (13,8), or between (20,7) and (13,8). It makes no difference, the result is exactly the same:
Actually, you really need  , so you can stop by saying that 
Now the equation of the circle is  where (h,k) is the center of the circle and r is the radius.
In this case, the equation of the circle is  .
For additional user-friendly explanation on this topic or most any topic , please see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look on my homepage for "MATH IN LIVING COLOR", and see "College Algebra", Section 2.04 The Circle. Or, for a more complete explanation, you can buy the College Algebra book for $30 on Ebay (search for "rapalje").
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