Question 690266
to find the equation for the circle with center 

({{{-5}}},{{{4}}})=({{{x}}},

{{{y}}}) and passing through the point

({{{-4}}},{{{-5}}})=({{{x[1]}}},{{{y[1]}}})


first find the radius squared:


radius = distance from center to the point:


{{{r^2 = ((4-(-5))^2 + (-5-(-4))^2) =(4+5)^2 + (-5+4)^2=9^2+(-1)^2=81+1=82}}}

passing through ({{{-4}}},{{{-5}}})=({{{x[1]}}},{{{y[1]}}})

{{{(x-x[1])^2 + (y-y[1])^2 =82}}} 

{{{(x-(-5))^2 + (y-4)^2 = 82 }}}

{{{(x+5)^2 + (y-4)^2 = 82 }}}


{{{drawing( 600, 600, -15, 15, -15, 15, 
         grid(1),circle(-5,4,0.2),circle(-4,-5,0.2), locate(-5,4-.2,"(-5,4)"), locate(-4,-5-.2,"(-4,-5)"),
         blue( circle( -5, 4, sqrt(82), 1 ) )
           
)}}}