Question

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

$2x^2-3xy+4y^2+2x+3y-5=0$

Short answer

The equation defines ellipse.

Step-by-step solution

Step 1. Given Information

The given equation is $2x^2-3xy+4y^2+2x+3y-5=0$

Here$A=2,B=-3,C=4$$A=2,B=-3,C=4$

Step 2. Identifying Conic

$$\begin{gathered} B^2-4AC={\left(-3\right)}^2-4\left(2\right)\left(4\right) \\ {B}^2-4AC=9-32=-23<0 \end{gathered}$$

The equation defines ellipse.