SOLUTION: write the equation of the information given. endpoints of a diameter are (6,9) and (20,7)

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Question 143181: write the equation of the information given.
endpoints of a diameter are (6,9) and (20,7)
Found 2 solutions by rapaljer, scott8148:
Answer by rapaljer(4671)   (Show Source): You can put this solution on YOUR website!
You forgot to say what kind of equation you need here. Is it the equation of a circle such that these are the endpoints of the diameter? Is it the equation of a line passing through the two points??

My guess is that you are probably finding the equation of a circle. 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").

R^2
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
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