Question 831032
given:

point ({{{2}}},{{{-4}}})

{{{x^2+y^2-6x+8y=-15}}} ..........first let see what we have here,

complete square

{{{(x^2-6x+_)+(y^2+8y+_)=-15}}}

{{{(x^2-6x+3^2)-3^2+(y^2+8y+2^2)-4^2=-15}}}

{{{(x-3)^2-9+(y+4)^2-16=-15}}}

{{{(x-3)^2+(y+4)^2=-15+9+16}}}

{{{ (x-3)^2+(y+4)^2=10}}}.........so, we have a circle with a center coordinates {{{h=3}}} and {{{k=-4}}}

so, the center is at point ({{{3}}},{{{-4}}})

since you are given a point ({{{2}}},{{{-4}}}), means that given point is {{{not}}} a center


{{{drawing( 600, 600, -10, 10, -10, 10,circle(3,-4,0.1),locate(3,-4,C(3,-4)), graph( 600, 600, -10, 10, -10, 10, sqrt(-(x-3)^2+10)-4,-sqrt(-(x-3)^2+10)-4)) }}}