Question

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

$9x^2+12xy+4y^2-x-y=0$

Short answer

The equation defines parabola.

Step-by-step solution

Step 1. Given Information

The given equation is $9x^2+12xy+4y^2-x-y=0$

Here$A=9,B=12,C=4$

Step 2. Identifying Conic

$$\begin{gathered} B^2-4AC={12}^2-4\left(9\right)\left(4\right) \\ {B}^2-4AC=144-144=0 \end{gathered}$$

The equation defines parabola.