Question 702648
{{{4x^2+y^2-48x-4y+48= 0}}}....reorder terms 


{{{4x^2-48x+y^2-4y+48= 0}}}...replace {{{48}}} with {{{144+4-100}}} 

{{{4x^2-48x+y^2-4y+144+4-100= 0}}}.......group

{{{(4x^2-48x+144)+(y^2-4y+4)-100=0}}}


{{{4(x^2-12x+36)+(y^2-4x+4)-100=0}}}....write {{{(x^2-12x+36)}}} as {{{(x-6)^2}}} and 

{{{(y^2-4x+4)}}} as {{{(y-2)^2}}}


{{{4(x-6)^2+(y-2)^2-100=0}}}


{{{4(x-6)^2+(y-2)^2=100}}}


{{{4(x-6)^2/100+(y-2)^2/100=100/100}}}


{{{cross(4)(x-6)^2/cross(100)25+(y-2)^2/100=1}}}


{{{(x-6)^2/25+(y-2)^2/100=1}}}


{{{(x-6)^2/5^2+(y-2)^2/10^2=1}}}....this is your ellipse with a center ({{{h}}},{{{k}}} at ({{{6}}},{{{2}}}, semi-minor axis length {{{a=5}}}, and semi-major axis length {{{b=10}}}