Eric D. answered • 04/19/19
Math, Computer Science, and standardized testing tutor
In general, the equation of a circle takes the form:
(x-a)2+(y-b)2 = r2
Where a is the x coordinate of the center of the circle, b is the y coordinate of the center of the circle, and r is the radius of the circle. First let's find the radius.
We know that the distance between A and B in the problem is the diameter, or two times the radius so let's find that distance.
dist(A to B) = sqrt( (Ax-Bx)2 + (Ay-By)2)
= sqrt((2-6)2+(3-1)2)
= sqrt(16 + 4)
= sqrt(20)
So the diameter is sqrt(20), and the radius is half of that which is sqrt(5).
(x-a)2+(y-b)2 = (sqrt(5))2
(x-a)2+(y-b)2 = 5
Next, find the center. To do so, get the slope between A and B and find the midpoint.The midpoint should be (4.2).
Now just plug back in those values for a and b to get:
(x-4)2+(y-2)2 = 5
