Question

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

$10x^2-12xy+4y^2-x-y-10=0$

Short answer

The equation defines ellipse.

Step-by-step solution

Step 1. Given Information

The given equation is $10x^2-12xy+4y^2-x-y-10=0$

Here$A=10,B=-12,C=4$

Step 2. Identifying Conic

$$\begin{gathered} B^2-4AC={\left(-12\right)}^2-4\left(10\right)\left(4\right) \\ {B}^2-4AC=144-160=-16<0 \end{gathered}$$

The equation defines ellipse.