Question

In Problems 43–52, identify the graph of each equation without applying a rotation of axes.

$3x^2-2xy+y^2+4x+2y-1=0$

Short answer

The equation defines ellipse.

Step-by-step solution

Step 1. Given Information

The given equation is $3x^2-2xy+y^2+4x+2y-1=0$

Here$A=3,B=-2,C=1$

Step 2. Identifying Conic

$$\begin{gathered} B^2-4AC={\left(-2\right)}^2-4\left(3\right)\left(1\right) \\ {B}^2-4AC=4-12=-8<0 \end{gathered}$$

The equation defines ellipse.