# What conic section does the equation −x+2y+x^2+xy+y^2=0 represent?

Sep 28, 2014

This equation is in near standard from. The terms have to be re-ordered.

$A {x}^{2} + B x y + C {y}^{2} + D x + E y + F = 0$

${x}^{2} + x y + {y}^{2} - x + 2 y = 0$

We need the coefficients $A$ and $C$ to make a determination.

$A = 1$
$C = 1$

$A = C$
$1 = 1$

This is a circle .