P and Q are endpoints, so the center of the circle would be the midway point.
A. The midpoint is found using:
(x1 + x2 /2 , y1 +y2 /2)
-10 + 4 = -6 /2 = -3
-2 + 6 = 4 /2 = 2
The center of the circle is at (-3,2)
B) The radius would be the distance from the midpoint to an end point.
Using the distance formula:
√((x2-x1)^2 + (y2-y1)^2)
√(4 - -3^2 + 6-2^2)
√(7^2 + 4^2)
√(49+16)
√65
C) Using the circle equation form of (x-h)^2 + (y-k)^2 = r^2
H,K is the center point found in part A and r is the radius found in part B.
The equation becomes (x-(-3))^2 + (y -2)^2 = √65^2
Which simplifies to: (x+3)^2 + (y-2)^2 = 65
