standard equation of a circle given endpoints of diameter are (-2,3) and (6,-4)

Question

standard equation of a circle given endpoints of diameter are (-2,3) and (6,-4) for my precal assignment, i just want to check my answer:) 

Answer 1

The center is the midpoint of the diameter.  So, center = ( (-2+6)/2, (-4+3)/2) = (2, -1/2)

 

The radius is the distance from the center to any point on the circle.

 

    So, radius = √ [(6-2)² + (-4+1/2)²] = √(16 + 49/4) = √(113/4) 

 

Equation of circle has the form (x-h)² + (y-k)² = r², where (h,k) is the center and r is the radius.

 

Equation of circle:  (x-2)² + (y+1/2)² = 113/4