# What conic section does the equation 2x^2+4xy+6y^2+6x+2y=6 represent?

Sep 28, 2014

First locate the coefficients for the ${x}^{2}$ term, $A$, and the ${y}^{2}$ term, $C$.

$A = 2$
$C = 6$

Characteristics of an ellipse.

$A \cdot C > 0$
$A \ne C$

$2 \cdot 6 > 0$ True
$2 \ne 6$ True

This is an ellipse .