Question

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

$x^2-7xy+3y^2-y-10=0$

Short answer

The equation defines hyperbola.

Step-by-step solution

Step 1. Given Information

The given equation is $x^2-7xy+3y^2-y-10=0$

Here$A=1,B=-7,C=3$

Step 2. Identifying Conic

$$\begin{gathered} B^2-4AC={\left(-7\right)}^2-4\left(1\right)\left(3\right) \\ {B}^2-4AC=49-4\left(1\right)\left(3\right)=27>0 \end{gathered}$$

The equation defines hyperbola.