Question 1169924
{{{8x^2+7y^2-32x+42y-17=0 }}}........group like variables and complete squares

{{{(8x^2-32x)+(7y^2+42y)-17=0}}}

{{{8(x^2-4x)+7(y^2+6y)-17=0}}}

{{{8(x^2-4x+b^2)-8b^2+7(y^2+6y+b^2)-7b^2-17=0}}}

{{{8(x^2-4x+2^2)-8*2^2+7(y^2+6y+3^2)-7*3^2-17=0}}}

{{{8(x-2)^2-32+7(y+3)^2-63-17=0}}}

{{{8(x-2)^2+7(y+3)^2-112=0}}}.........divide by{{{ 112}}}

{{{8(x-2)^2/112+7(y+3)^2/112-112/112=0}}}

{{{(x-2)^2/14+(y+3)^2/16-1=0}}}

{{{(x-2)^2/14+(y+3)^2/16=1}}} ....-> {{{ellipse}}}

 center is at ({{{2}}},{{{-3}}})

semimajor axis length | {{{sqrt(16)=4}}}
semiminor axis length | {{{sqrt(14)}}}≈{{{3.7}}}


{{{drawing( 600, 600, -10, 10, -10, 10,

circle(2,-3,.12),locate(2,-3,C(2,-3)),
 graph( 600, 600, -10, 10, -10, 10,- sqrt(16(1-(x-2)^2/14))-3,sqrt(16(1-(x-2)^2/14))-3)) }}}