Question 945002
On the coordinate plane, the formula becomes {{{(x-h)^2+(y-k)^2=r^2}}}

   {{{ h}}} and {{{k}}} are the {{{x}}} and {{{y}}} coordinates of the center of the circle , and {{{r}}} is radius

Three points on the circle: ({{{-15}}},{{{-9}}}), ({{{1}}},{{{-9}}}), and ({{{-15}}},{{{3}}}).

use points to find{{{ h}}}, {{{k}}}, and {{{r}}}

{{{(x-h)^2+(y-k)^2=r^2}}} ......for ({{{-15}}},{{{-9}}}),

{{{(-15-h)^2+(-9-k)^2=r^2 }}}

{{{h^2+30h+k^2+18k+306=r^2}}} ............eq.1


{{{(x-h)^2+(y-k)^2=r^2}}} ......for ({{{1}}},{{{-9}}}),

{{{h^2-2h+18k+k^2+82=r^2 }}} ............eq.2


{{{(x-h)^2+(y-k)^2=r^2}}} ......for ({{{-15}}},{{{3}}}),

{{{(-15-h)^2+(3-k)^2=r^2 }}}

{{{h^2+30h+k^2-6k+234=r^2}}} ............eq.3

system is:

{{{h^2+30h+k^2+18k+306=r^2}}} ............eq.1
{{{h^2-2h+18k+k^2+82=r^2 }}}............eq.2
{{{h^2+30h+k^2-6k+234=r^2}}} ............eq.3
----------------------------------------------------------

subtract eq.3 from eq.1

{{{h^2+30h+k^2+18k+306-(h^2+30h+k^2-6k+234)=r^2 -r^2}}}

{{{h^2+30h+k^2+18k+306-h^2-30h-k^2+6k-234=0}}}

{{{18k+306+6k-234=0}}}

{{{24k+72=0}}}

{{{24k=-72}}}

{{{k=-72/24}}}

{{{highlight(k=-3)}}}

go to

{{{h^2-2h+18k+k^2+82=r^2 }}} ............eq.2 substitute {{{k}}}


{{{h^2-2h+18(-3)+(-3)^2+82=r^2 }}}

{{{h^2-2h-54+9+82=r^2 }}}

{{{h^2-2h+37=r^2}}}.............2a  

go to

{{{h^2+30h+k^2-6k+234=r^2}}} ............eq.3 substitute {{{k}}} and {{{r^2}}}

{{{cross(h^2)+30h+(-3)^2-6(-3)+234=cross(h^2)-2h+37}}}

{{{30h+9+18+234=-2h+37}}}

{{{30h+261=-2h+37}}}

{{{30h+2h=-261+37}}}

{{{32h=-224}}}

{{{h=-224/32}}}

{{{highlight(h=-7)}}}

go to 

{{{h^2-2h+18k+k^2+82=r^2 }}} ............eq.2 substitute {{{k}}} and {{{h}}}  and solve for {{{r}}}

{{{(-7)^2-2(-7)+18(-3)+(-3)^2+82=r^2 }}}

{{{49+14-54+9+82=r^2 }}}

{{{100=r^2 }}}

{{{highlight(r =10)}}}


so, your equation is  {{{(x+7)^2+(y+3)^2=100}}}


{{{drawing( 600, 600, -25, 25, -25, 25,circle(-7,-3,10),circle(-7,-3,.2),
circle(-15,-9,.2),locate(-15,-9,p(-15,-9)),
circle(-15,3,.2),locate(-15,3,p(-15,3)), 
circle(1,-9,.2),locate(1,-9,p(1,-9)), locate(-7,-3,C(-7,-3)),
graph( 600, 600, -25, 25, -25, 25, 0)) }}}