A circle passes through the points \((-2,0)\), \((2,0)\), and \((3,2)\). Find the center of the circle. Enter your answer as an ordered pair.
Thank you!
+23246 A = (-2, 0)
B = (2, 0)
C = (3, 2)
Since there is a right angle at B, AC must be a diameter of the circle.
Therefore, the center of the circle is the midpoint of AC.
The midpoint of AC = ( (-2 + 3)/2, (0 + 2)/2 ) = ( 1/2, 1 )
+23246 You're right -- I messed up -- I thought (3,2) was (2,3) -- my fault ...
+128407 Find the midpoint of (-2,0) and (2,0) = (0,0)
The line perpendicular to this point is just the x axis and has the equation x = 0
Find the midpoint of (2,0) and(3,2) = [ 3+2/2, 2+0/2) = (5/2, 1)
The slope of the line through these points = [ 2-0]/[3 - 2] = 2
And the slope of a perpendicular line passing through the midpoint we just found has the slope -1/2
The equation of this line is
y = (-1/2) ( x - 5/2) + 1
Letting x = 0 we can find the y coordinate of the center of the circle
y = (-1/2)(0 -5/2) + 1 = 5/4 + 1 = 9/4
So...the center of the circle is (0, 9/4)
And the square of the radius is 2^2 + (9/4)^2 = 4+ 81/16 = 145/16
Here's the graph https://www.desmos.com/calculator/wdbs8u2edh
