Question 813344
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
circle whose diameter has endpoints (4, -1) and (-6, 7).
D = {{{sqrt ((x[1]-x[2])^2+(y[1]-y[2])^2))}}}
D = {{{sqrt ((10^2+ (-8)^2)) = sqrt(164) = 2sqrt(41)}}}
r = {{{sqrt(41)}}}
Midpoint Pt(x,y):  ( {{{(x[1] + x[2])/2}}}, {{{(y[1] + y[2])/2  )}}})

Midpoint Pt(x,y):  (-2/2 , 6/2)  0r  (-1,3)
Standard Form of an Equation of a Circle is {{{(x-h)^2 + (y-k)^2 = r^2}}} 
where Pt(h,k) is the center and r is the radius
{{{(x+1)^2 + (y-3)^2 = 41}}} 
{{{drawing(300,300, -10, 10, -10, 10,  grid(1),
circle(4, -1,0.4),
circle(-6, 7,0.4),
circle(-1, 3,0.4),
circle(-1, 3,sqrt(41)),
graph( 300, 300,  -10, 10, -10, 10,0))}}}