Question 143180
Assuming that the problem is to find the equation of a circle with end points of diameter at these two points, the first step is to find the center of the circle, which is the midpoint of these two points.  To find the midpoint of two points, it's like the average of the x coordinates (add together and divide by 2), and the average of the y coordinate.


(6,9) and (20,7)

{{{x=(6+20)/2=26/2=13}}}
{{{y=(9+7)/2=16/2=8}}}


Next, find the radius, which is the distance from the center to either endpoint.  For example, between (6,9) and (13,8), or between (20,7) and (13,8).  It makes no difference, the result is exactly the same:
{{{distance= sqrt( (xdiff)^2 + (ydiff)^2 ) }}}
{{{radius = sqrt(7^2+1^2) }}}
{{{radius = sqrt(49+1) }}}
{{{radius = sqrt(50) }}}


Actually, you really need {{{r^2}}}, so you can stop by saying that {{{r^2= 50}}}


Now the equation of the circle is {{{ (x-h)^2 + (y-k)^2 = r^2 }}} where (h,k) is the center of the circle and r is the radius.


In this case, the equation of the circle is {{{(x-13)^2+(y-8)^2= 50 }}}.


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R^2