Question

Determine the equation of a circle having a diameter with endpoints at (12,-14) and(2,4)

Answer 1

Center of a circle is a midpoint of line connecting two endpoints so center is:
(12,-14) (2,4) we divide those two points by two 
C(a,b)- center
C(a,b)=((12+2)/2),(-14+4)/2)=(7,-5)
Radius is the distance from the center to any point on the circle:
we take point (2,4)
r=$\sqrt{ (7-2)^{2} + (-5-4)^{2} } = \sqrt{25+81} = \sqrt{106}$