SOLUTION: Find the equation of a circle that has a diameter with the endpoints given by the points A (-5,4) and (7,9)

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Question 1174553: Find the equation of a circle that has a diameter with the endpoints given by the points A (-5,4) and (7,9)
Found 3 solutions by ewatrrr, MathLover1, ikleyn:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
the equation of a circle that has a diameter with the endpoints 
(-5,4)   D = sqrt%28+%28-5%29%5E2++%2B+%2812%29%5E2%29 = 13   C(1,6.5 )  P(2/2, 13/2)
(7,9)
       Circle:   (x-1)^2 + (y-6.5)^2 = 6.5^2

Wish You the Best in your Studies.


Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Find the equation of a circle that has a diameter with the endpoints given by the points A (-5,4) and (7,9)
the length of a diameter is equal to distance between given points:
Solved by pluggable solver: Distance Between 2 points
The distance formula is sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29. Plug in the numbers,
sqrt%28%28%287-%28-5%29%29%5E2%29%2B%28%289-%284%29%29%5E2%29%29
sqrt%2812%5E2%2B5%5E2%29 The distance is 13.


d=13 => radius is r=13%2F2
the center of a circle is half way between given points
C (%28-5%2B7%29%2F2,%284%2B9%29%2F2)
C (1,13%2F2) => h=1 and k=13%2F2
the equation of a circle is:
%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2
%28x-1%29%5E2%2B%28y-13%2F2%29%5E2=%2813%2F2%29%5E2
x%5E2+-+2+x+%2B+1%2By%5E2+-+13+y+%2B+169%2F4=169%2F4
x%5E2+-+2+x+%2B+1%2By%5E2+-+13+y+%2B+169%2F4-169%2F4=0
x%5E2+-+2+x+%2B+y%5E2+-+13+y+%2B+1+=+0





Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.

From two ladies, you have the same equation for the circle, but two different plots.

Now you need to guess which one of the two plots is correct . . . (if any) . . .


I will help you (!)


        The plot which is tangent to x- axis is correct.

                The other plot is  INCORRECT.