SOLUTION: Find the standard form for the equation of a circle with equation (x-h)^2+ (y-k)^2=r2 with a diameter that has endpoints (-5,8) and (9,4) i got 53 for the radio and found

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Question 785341: Find the standard form for the equation of a circle with equation (x-h)^2+ (y-k)^2=r2

with a diameter that has endpoints (-5,8) and (9,4)
i got 53 for the radio and found the midpoint coordinates (2,6) however my answer is still wrong, please help me!

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
the equation of a circle with equation

with a diameter that has endpoints (,) and (,)
first find diameter which is equal to distance between two given points:
Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (-5, 8), we can say (x1, y1) = (-5, 8)
So ,


Since the second point is (9, 4), we can also say (x2, y2) = (9, 4)
So ,


Put this all together to get: , , , and

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Now use the distance formula to find the distance between the two points (-5, 8) and (9, 4)






Plug in , , , and






















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Answer:


The distance between the two points (-5, 8) and (9, 4) is exactly units


The approximate distance between the two points is about 14.560219778561 units



So again,


Exact Distance: units


Approximate Distance: units




since
now we know that radius is
now, find coordinates of the center which will be midpoint of diameter:
Solved by pluggable solver: Midpoint


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (-5, 8), we can say (x1, y1) = (-5, 8)
So ,


Since the second point is (9, 4), we can also say (x2, y2) = (9, 4)
So ,


Put this all together to get: , , , and

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Finding the x coordinate of the midpoint: Add up the corresponding x coordinates x1 and x2 and divide that sum by 2


X Coordinate of Midpoint =


X Coordinate of Midpoint =


X Coordinate of Midpoint =


X Coordinate of Midpoint =



So the x coordinate of the midpoint is 2


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Finding the y coordinate of the midpoint: Add up the corresponding y coordinates y1 and y2 and divide that sum by 2


Y Coordinate of Midpoint =


Y Coordinate of Midpoint =


Y Coordinate of Midpoint =


Y Coordinate of Midpoint =


So the y coordinate of the midpoint is 6



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Summary:


The midpoint of the segment joining the two points (-5, 8) and (9, 4) is (2, 6).


So the answer is (2, 6)




as you can see, the midpoint of the segment joining the two points (,) and (,) is (, ) which means and
so, equation of a circle will be:





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