Question 698810
{{{4x^2+9y^2-64x+162y+949=0}}}

{{{(4x^2-64x)+(9y^2+162y)+949=0}}}....write {{{949 }}} as {{{256+729-36}}} and complete square 

{{{(4x^2-64x) }}} so; use {{{256}}} to write {{{-64}}} as {{{2ab}}} where

 {{{2a=256/64=4}}} and {{{b=sqrt(256)=16}}}; than you will have {{{2ab=-128}}}

 and (4x^2-128x+256) ...do same with  (9y^2+162y) and you will get 

{{{9y^2+324y+729}}}


{{{(4x^2-128x+256)+(9y^2+324y+729)-36=0}}}


{{{(4x^2-128x+256)+(9y^2+324y+729)-36=0}}}


{{{4(x^2-32x+64)+9(y^2+36y+81)-36=0}}}


{{{4(x-8)^2+9(y+9)^2-36=0}}}


{{{4(x-8)^2+9(y+9)^2=36}}}.....both sides divide by {{{36}}}


{{{4(x-8)^2/36+9(y+9)^2/36=36/36}}}


{{{(x-8)^2/9+(y+9)^2/4=1}}}