SOLUTION: If the endpoints of a diameter of a circle are (4,3)and (-3,5), what is the equation of the circle? This is my answer is this right, if not what is? Answer (5-3)^2+(-3-4)^2 =2

Question 460962: If the endpoints of a diameter of a circle are (4,3)and (-3,5), what is the equation of the circle?
This is my answer is this right, if not what is?
Answer
(5-3)^2+(-3-4)^2
=2^2+(-7)^2
=4+49
=53
radius=53/2
midpoint : (1/2, 4)
equation of the circle=(x-1/2)^2+(y-4)^2=53/4
Found 2 solutions by jim_thompson5910, Gogonati:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The radius is actually , which will make . You forgot to take the square root of 53 in the last step.

Anyways, the equation you have is the correct one nonetheless. Good job.
Answer by Gogonati(855) (Show Source): You can put this solution on YOUR website!
Since we know the coordinates of the endpoints of the diameter we can find the coordinate of the center:
and , thus the circle is centered at
(1/2, 4). Now we need to find out the radius of the circle:
. As we know the equation of the circle in
standard form is : , substituting our values we get:
, which is the equation of our circle.
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