Question 941871
Find an equation of the circle with endpoints of a diameter are
P({{{-1}}}, {{{3}}}) and QP({{{5}}}, {{{-7}}}) 

an equation of the circle  is {{{(x -h)^2 + (y - k)^2 = r^2}}}; so, we need  the coordinates of the center  ({{{h }}},{{{k}}}) and the radius {{{r}}}

First find the coordinates of the center : ({{{h }}},{{{k}}})

=>{{{ x=h = (x1+x2)/2 = (-1+5) /2 = 4/2=2}}}

=>{{{ y =k= (y1+y2)/2 = (3-7) /2 = -4/2=-2}}}

so, C ({{{2}}},{{{-2}}}) is the center 

now find the radius ( u can find its length by taking the distance between one endpoint and C )

take     ({{{2}}},{{{-2}}}) and P({{{-1}}}, {{{3}}}) 

=> {{{r = sqrt ( (2-1)^2 + (-2-3)^2 ) }}}
= >{{{r =sqrt (1+25) }}}

= >{{{r =sqrt (26) }}}

= >{{{r =5.83}}}

hence the equation is :

{{{(x - 2)^2 + (y+2)^2 = 26 }}}


{{{drawing( 600, 600, -15, 15, -15, 15,
green(circle(2,-2,5.83)),circle(-1,3,.13), circle(5,-7,.13),circle(2,-2,.13),
locate(-1,3,P(-1,3)),locate(5,-7,Q(5,-7)),locate(2,-2,C(2,-2)),
graph( 600, 600, -15, 15, -15, 15, 0)) }}}