Question 739366
it is an ellipse



{{{5x^2+2y^2+30x-16y+67=0}}}........group like terms

{{{(5x^2+30x)+(2y^2-16y)+67=0}}}....complete square

{{{(5x^2+30x+___)+(2y^2-16y+___)+67=0}}}

{{{(5x^2+30x+45)-45+(2y^2-16y+32)-32+67=0}}}

{{{(5x^2+30x+45)+(2y^2-16y+32)-10=0}}}......factor out {{{5}}} and {{{2}}}

{{{5(x^2+6x+9)+2(y^2-8y+16)-10=0}}}

{{{5(x+3)^2+2(y-4)^2-10=0}}}.......=>...{{{h=-3}}} and {{{k=4}}}

the center: ({{{-3}}},{{{4}}})


{{{ drawing ( 500, 500, -10, 10, -10, 10,circle(-3,4,0.1),graph( 500, 500, -10, 10, -10, 10,sqrt(-(5/2)(x+3)^2+5)+4,-sqrt(-(5/2)(x+3)^2+5)+4)) }}}