Question

Trace the following central conics.
$x^2+xy+y^2+x+y+1=0.$

Answer 1

$x^2+xy+y^2+x+y+1=0$

General eqn of a conic : ${ax}^2+2hxy+{by}^2+2gx+2fy+c=0$

Comparing both equations,

$a=1,2h=1,b=1,2g=1,2f=1,c=1$

$h^2=1/4$ and $ab=1$

$h^2<ab$

Hence, conic is an ellipse.