Question 933775
{{{x^2/36+y^2/16=1}}} always when you see it's equal to {{{1}}}, you know it's an ellipse

Standard equation of an ellipse is:


{{{(x-h)^2/a^2 + (y-k)^2/b^2 = 1}}} (if the major axis is horizontal).


{{{(x-h)^2/b^2 + (y-k)^2/a^2 = 1}}} (if the major axis is vertical). 

since your ellipse doesn't have any value for {{{h}}} and {{{k}}}, means {{{h=0}}} and {{{k=0}}} and the center is in origin ({{{0}}},{{{0}}})

{{{a}}} is the {{{horizontal}}} semi-axis and {{{b}}} the vertical semi-axis 

since your {{{a=sqrt(36)=highlight(6)}}} and {{{b=sqrt(16)=highlight(4)}}}, we can see that {{{a>b}}}, so, the standard equation of your ellipse is:

{{{(x-0)^2/36 + (y-0)^2/16 = 1}}} (the major axis is horizontal)



{{{ drawing( 400, 400, -10, 10, -10, 10, grid( 1 ),circle(0,0,.13), blue( ellipse( 0, 0, 12, 8 ) ) ) }}}