An archeologist found the remains of an ancient wheel,which she placed on a grid.If an arc of the wheel passes through A(-8,0),B(-3,4),and C(8,0),locate the center of the wheel,and the standard equation of the circle defining its boundary.
+128406 If we have the points A= ( -8,0) and C = ( 8,0) on the circle....then AC will form a chord in the circle
This means that the center of the circle will have the coordinates (0,a)
And the distance from the center to B will be the same distance from the center to C
So we have this
(-3)^2 + (4-a)^2 = (8)^2 + ( a)^2
9 + 16 - 8a + a^2 = 64 + a^2 simplify
-39 = 8a
a = -39/8
The center is (0, -39/8)
The radius ^2 = ( 8)^2 + ( -39/8)^2 = 5617/64
The equation is
x^2 + ( y + 39/8)^2 = 5617/64
See the graph here : https://www.desmos.com/calculator/ul4b4frbtz
