Question 694971
Ellipse.
{{{x^2+4y^2-6x+20y-2=0}}} --> {{{x^2-6x+4y^2+20y=2}}} --> {{{x^2-6x+9+4y^2+20y+25=2+9+25}}} --> {{{(x^2-6x+9)+4(y^2+5y+25/4)=36}}} --> {{{(x-3)^2+4(y+5/2)^2=36}}} --> {{{(x-3)^2/36+(y+5/2)^2/9=1}}}
It is centered at (3,-5/2), with a semi-major axis of length 6, parallel to the x-axis, and a semi-minor axis of length 3, parallel to the y axis.
{{{graph(300,150,-4,10,-6,1,(sqrt(27-x^2+6x)-5)/2,(-sqrt(27-x^2+6x)-5)/2)}}}